Other fleets
Unfortunatley, that seems to be (currently) all I have for Imperial fleets in terms of hard facts (such as they are). At this point things become much more conjectural., but not totally speculative. The "other fleets" category includes the following: "Planetary defence force" navies (which I already covered in some detail, but I'll reiterate here), the Arbites, the ministorum/ecclesiarchy (Sororitas and Frateris mainly.), the Guard, the Rogue Traders, the Adeptus Mechanicus, and of course the Inquisition. Not neccesarily in that order.
Planetary Defense Fleets
As already mentioned, PDF fleets probably represent the "largest" accumulation of ships, although their limited/nonexistent warp-capable nature and diversity make them virtually impossible to unify or coordinate. Numbers are almost certainly in the "millions" - most if not nearly all planets in the Imperium are bound to have SOME form of system defense, and logically to include defense ships.
As per Battlefleet Gothic, Port Maw had "hundreds" of system defense ships, which probably represents an extraordinary concentration (given Porrt Maw was a sector/segmentum naval base.)
The planet Ultramar from "Warriors of Ultramar" had dozens (as did MacCragge) and could be considered representative of a "major" world (say a Hive world or Forge world) It could be safe to say therefore that the PDF fleets probably comprise a dozen or two mobile "system ships" (monitors and patrol ships both) on average, plus whatever fixed defenses are established.
As an order of magntiude estimate (assuming one million planets, possibly as many as "ten million" if you take millions literally), this would mean the PDF fleets total tens of millions of ships, ,possibly hundreds of millions.
But no more than a few billion (!) barring extreme upper limit calcs.
Guard units
A few sources (Inquisition War, Soul Drinkers) make indirect hints that the Imperial Guard may have some ships under their command. Presumably they are not directly "owned" by the Guard (few truly "own" a ship of their own in the imperium) but ships (probably transports, but possibly some escorts.) on loan to the Guard. A good (possible) example of this would be in the Gaunt's Ghosts novels, where Gaunt has a frigate assigned to him for his use (First nad only describes it as "his" Flagship.) There's also the Phantine, ,who are known to use fighters (normally a "Navy" role/privelege.)
While technically this can be (correctly) seen as a violation of the separation between Army and Navy that is meant to prevent another Horus Heresy, it does not represent as great a danger as one might think. For one thing, the "ships" known or probably assigned ot the Guard are not going to be the biggest or most powerful (smaller than a cruiser or battleship, and probably even some escorts) and therefore something the Navy (or other forces if need be) could easily deal with. Moreover, any "warship" could not carry more than a regiment (at best, and probably a small one at that) at best, so their ability to attack or conquer a planet (or defeat a planet's defenses) are clearly limited as well. A troop transport COULD carry more troops, arguably, but its defenses would be weaker (and it would be easier to destroy by the Navy, Space Marines, etc.)
What "Guard ships" probably represent are what amounts to specialized "rapid reaction" forces in a similar vein as to what the Space Marines and Arbites have - a limited number of small ships designed to fufill a specific and limited role. While a minor threat, its not one that would represent a scale of danger as seen in the Heresy. The vast majority of regiments probably still require separate transportation to be provided by the Navy, or are attached to other groups (the Inquisition, Space Marines, Rogue Traders, etc.) or serving as Garrison troops.
Adeptus Arbites
"Space Fleet" and the "Codex Imperialis" both mention (but do not clarify) that the Arbites have their own fleets. Understandable, given their role as a "galactic police force". The vessels are only ever outlined once to my knowledge, in Execution hour, where they use a
Punisher-class Strike cruiser. If they have strike cruisers, its also reasonable that they probably have escort-class vessels as well, and probably transports of their own (implied by Codex Imperialis.) These ships are used to supplement planetary assault, hunting pirates, rebels and criminals, and to police/protect systems or territories.
It is never known if they have battleships, but
Codex Imperialis implies they are capable of chasing down "Admirals of the fleet", which would imply they have some sort of heavier warship than a cruiser. In any case, they (like the Inquisition) are able to requisition forces of both the Guard AND Navy to augment their own, so they can increase their own figures by these means (And it happens in Execution Hour.)
Numbers aren't known, but its not unreasonable to expect them to have similar numbers as the Astartes. Given their presence throughout the Imperium, they probably have at least a handful of cruisers and escorts per sector - tens of thousands of ships minimum is quite likely, but probably more, given the "system security" needs and the implied "local" ranges. Of course, they are bound to have far fewer ships then the navy (10% or less of the Navy's warp-capable numbers again, "tens of thousands" of ships easily.)
Inquisition
The Inquisition, having a little bit of everything in the Imperium (ground troops, space marines, etc.) also have their own fleets. Each inquisitor is known to generally have his own conveyance (more influential ones can have more than one, in fact. Especially Lord Inquisitors) much in the same way they can assemble virtual armies of their own. But in addition to "personal" assets, the Inquistion has its own warships (like they do the Chambers militant and the storm troopers) who are not part of any one Inquisitor's retinue. Colloquially dubbed "black ships" in BFG (a term which has admittedly been corrupted throughout time)
The "Black ships" as they are dubbed, serve mainly as transportation and support vessels for the Inquisitional forcees, much in the same way Battle barges and strike cruisers do. The BFG version is described as a strike cruiser on a battlecruiser hull - quite probably the largest known "official" ship owned by the Inquisition (IE not "loaned" to them) outside of the Chambers militant battle barges. Whether they have battleships of their own (not borrowed) is unknown (and probably irrelevant.) but if they do, they're probably one of the most powerful ships around (aside from anything the AM might be hiding away.) The Eisenhorn novels imply the Inquisition DOES keep "Black ships" of cruiser class around as well. And its likely they have their own escort squadrons (who doesn't?)
"Black ships" have also, of course, meant those vessels designed to collect and ferry psykers to Earth for training and/or consumption by the GeOM.
In addition to that, the Space Marine chapters of the various Ordos (such as the Malleus' Grey Knights) seem to have their own battle barges, strike cruisers, and escrots, which also can be included in the Inquisition's numbers.
And, of course, the Inquisition can requisition ships from the Navy if they choose to, up to and including battleships. (As I recall, they have battleships from other battle fleets on permanant loan - painted black.) Which would not be "officially" counted here.
Numerically, the "personal" vessels of the Inquisition can probably number tens or hundreds of thousand or even millions, depending on how many Inquisitors one believes there are (I tend to believe the higher end ot fhe scale.) Not all of these are going to be "Warships" of any kind, but many are probably large enough to be warp-capable.
The Chambers militant can probably add at least six to ten battle barges, several dozen strike cruisers, and scores of escorts to that roster.
The "Black ship" fleet is unknown, but probably matches or exceeds the numbers of other factions (tens to hundreds of thousands.) It may even potentially match the Navy, though this is debatable.
Adeptus Mechanicus
Of all the factions in the Imperium, only the Adeptus Mechanicus and the astartes have ships that match or exceed Imperial Navy vessels, and of the two the Mechanicus ones are probably much more massive in terms of sheer volume (IE the 16 km conveyor from First and Only.) The Mechanicus has many sorts of vessels - from conveyors and transports dedicated to transferring their military forces (TechGuard and skitarii as well as Titan Legions) and other resources as well as research ships and the Explorator vessels. Not only are they some of the largest, but they are bound to be some of the most technologically sophisticated (moreso than the Navy, at least.) Some vessels can actually move prefab factories facilities (such as in Execution hour)
As a rule, their vessels seem to be multi-role in nature, and they do not seem to possess dedicated warships. However, given the sheer size of some (many) of the vessels, they probably CAN carry considerable firepower despite being designed for other purposes (transportation). It is also not unreasonable, if not likely, that the Adeptus Mechanicus keeps secret the true extent of the capabilities of their ships secret, the same way they do with others, and thus their ships could be more than a match for the Navy (if it came to that.) In any even,t since they control all the forge worlds, they doubtless can build warships if they chose to, in any event (they're already building for everyone else, as it is.)
This also means numbers are hard to come by but probably irrelevant.
Tens of thousands is a safe minimum, but they could easily come close to or match the Navy (merchan and warships) in size.
Sororitas and Frateris vessels
Only mentioned in
Iron Hands (sororitas) and the Eisenhorn books (Frateris), though
Codex Imperialis does describe the Sororitas having their own fleets also, and the "Space Fleet" essay mentions that the Priesthood maintains a small number of ships for personal use (presumably including warships.) Numerically, there is very little to go on.
According to "sisters of Battle" codex, the Sisterhood's orders only number in the thousands (with six Orders), and generally do not exceed 10,000 (although they admit the numbers can vary dramatically.) This would imply very small fleets (assuming they transportt a company or its equivalent apiece) would suggest hundreds or thousands of ships at best. It's also possible the Sororitas numbers were changed (upwards, I imagine. Tens of thousands seems too few for its roles, much the same way the Space marine fleets are somewhat small for theirs.)
The Frateris presumably do not "own" any ships directly, as they are not officially part of the Ecclesiarchy, but presumably are under the control of the Priesthood and "coincidentally" are crewed by volunteers. No idea on their numbers, but they may potentially match the other factions (arbites and astartes, that is.)
Rogue Traders
Rogue Traders, of course, have vessels of their own. Few if any actually "own" these ships, but they come as part of their charter or may be "loaned" to the Traders from other sources (mainly the merchant and naval side of things, especially the navy or naval reserves.) Most Rogue Traders command small ships (cruisers and escorts or their equivalent, armed merchant ships, freighters and transprots, and the like.) Almost all are well armed (Although not "true" military vessels save those they borrow/acquire from the Navy, that is.) and some may be unconventionally outfitted (especially if operating under Inquisitorial fiat - eg Ravenor.)
In terms of numbers, the Rogue Traders are never formally outlined excecpt in Space Fleet mentioning "hundreds", but this is probably unlikely in "recent" editions (again, the numbers in "Space fleet" were drastically underestimated.) Thousands seems likely, with a rogue Trader on average probably owning a few vessels (such as in Rogue Star), but in some cases a Rogue Trader may run dozens or hundreds of ships - including ships as large as a battleship (although this is probably rare and requires real cooperation between the RT and the navy)
Numbers, while hard to come by, probably are not drastically important in this case, as the Rogue Traders are the most likely of any other faction to have their vessels loaned to them from the other fleets of the Imperium, so they probably have few "personal" vessels.
Officio Assasinorum
They have ships, according to "Space Fleet", but numbers and type and capability are unknown. Probably quite small, though.
Navigators
To my knowledge never directly described except for a brief mention in "space fleet" (as Privately owned ships), although since every other major faction in the Imperium has at least SOME ships, I expect the Navigators do (some warp capable, probably not warships, but also probably system defense vessels for their own territories.)
Privately-owned ships
Space fleet mentions "several thousand" privately owned ships registered to families, individuals, or trading cartels. It should be noted, however, that given how they under-estimate fleet and merchant numbers in
Space fleet, these figures could be at least an order of magntidue higher (tens of thousands of ships.) They are unliekly to be warships, but probably more armed merchant cruisers.
Fighters and attack craft "ordnance"
Fighters (which are substantially larger than their Imperial counterparts) can be quite large (close to or over 100+ meters, as per First and Only) often representing small "capital ships" of their own. Earlier novels (Inquisition War and Eye of Terror) also featured "Cobra class" attack ships (pre BFG cobra destroyers, really) that were sublight "parasite" vessels.
Other novels such as "dark angels" and Caves of Ice feature drop ships and shuttles and transports that are hundreds of meters long (and shuttles/transports are part of attack craft, remember.) As such, like the "PDF fleets" and "patrol ships" (see below), these are not counted but probably represent massive numbers (tens or hundreds of millions.
Probably more, given their definitively smaller size.)
These assets also probably qualify as part of "PDF" fleets too (which will further augment their numbers.)
Non-Battlegroup Naval forces
As noted in the BFG core book, there are numerous (smaller) vessels not
included in a battlefleets numbers, including patrol ships. They are also mentioned here
BFG mag 16, page 6 wrote:
Terrifying monuments and uninhabited, abandoned cities across worlds once ravaged by war stand as totems to what has passed there, while the sight of ever-ready patrol groups, battlefleets and infantry regiments prowling the stars serve as a constant reminder that wars which may have raged and burned out centuries before still flicker brightly enough to return and engulf Mankind at any moment.
The Soul drinkers novels, IIRC, also mention patrol ships, as does Eisenhorn, but not in any great detail.
These forces are not "officially" apartt of the batlte-fleet. They are presumably warp capable to some degree (albeit short ranged/local in all probability) and mostly designed for scouting/recon and dealing with small forces (pirates and smugglers) much like the arbites fleet. They are also thus probably smaller and less powerful (more like a system defense/patrol ships if anything.) But they are also probably present in greater numbers as well (millions if not tens of millions.) These may also represent hte "short ranged warp capable" vessels apartt of a PDF I speculated on earlier.
Reserve fleets
Falkenhayn mentioned these, but I figured its worth covering them here:
BFG armada page 29 wrote:
As with all highly militarised zones, it is important for the Imperial Navy to maintain substantial reserves of vessels around the eye of Terror, ,ready to deploy as reinforcecments should the need arise. Whilst it is possible to keep the vessels themselves ready in this manner, Battlefleet Obscura simply does not possess the manpower to keep reserve crews stationed aboard these vessels as well. Instead, whole shipyards are filled with rows of silent, inactive vessels, often representing classes of ship now outdated or scarce. In times of great need these ships will then be grought into serveice and crewed with sialors from destroyed or crippled vessels or even with hastily mustered new recruits.
This tells us that the Imperium's "active" fleet does not represent its WHOLE ship strength (aside from repairs or rebuilds and new construction) - they evidently have large numbers of ships in mothballs for emergencies.
As Falkenhayn noted, this probably means the numbers I outlined above can be doubled, trpled, or more (hundreds of thousands or millions more ships.)
It is worth noting, of course, ,that while these ships are there, they probably represent a lower quality in terms of design/capability and crews in many cases, for the reasons outlined in the quote. Nonetheless, in emergencies it indicates the Imperium can put forth substantially more warships should they need to. The trade off in doing so, however, is probably not just in quality, but in logistics (There's no guarantee their infrastructure or transporrt capability could neccesarily accomodate THAT many ships, for example..)
Conclusion
PDF, parasite and "patrol/recon" vessels aside, the ships of the Adeptus Mechanicus, the Adeptus ARbites, the Adeptus Astartes and the Inquisition collectively form a not-insignificant addition of vessels to the Imperium's overall (active) military strength, particularily since many of these groups tend to be better armed/equipped than the Navy is (Inquisition, AA, and AM in particular.) The Sorotias/Frateris
May contribute significantly, but that is unknown, as is how (if in any way) the Guard or Rogue Traders may contribute. Other than that, the rest are largely irrelevant.
PDF navies, parasite/ordnance craft and the "patrol" ships all probably represent less firepower "per ship" than any navy vessel, but their greater numbers doubtless make up for this, and in a war those forceces provide a valuable defensive edge. The Arbites serve a useful defensive role, while the Astartes can do both offense AND defense (its access to specialized Exterminatus ordnance can make them very good offensively.) The Inquisition can likewise serve both ends as needed, giving the Imperium and its Navy added flexibility. Reserve fleets, lastly, help offset the relatively slow construction rates by giving the Imperium a substantial "buffer" of usable warships.