The 4.86 introduction mentioned House military sizes. I remember just battleship numbers:
-Gallia: 500, 150 are invading Sirius;
-Liberty: not mentoned. Has almost as twice more as Rheinland - approximately 150;
-Rheinland: about 80;
-Bretonia: 55 - including 5 Exile battleships (yes, five. Not two. 2 are stationed);
-Kusari: beaten to the ground, probably has less than Bretonia, but more than Corsairs and Outcasts. 40 by my opinion.
-Corsairs: about 20, maybe less;
-Outcasts: about 10, fifteen if we're optimistic;
-Hessians: a bit less than the Outcasts;
-Nomads: most of their fleet is destroyed by a tennis ball sized artifact. They are also in war with everybody. A meager fleet is in their <strike>hands</strike> tentacles, even smaller after the Toledo conflict;
-Zoners: not a lot. Certainly more than 3 (including that big-huge-pre-jinkusu-alien-Persephone-thing);
-The Council: I separated them because I don't know a lot about them. Their fleet size is probably near that of the Corsairs or Outcasts. Maybe bigger. They managed to hold Gallic forces for a long time, didn't they?
I didn't include anybody else because they are out of the "strong list". But, battleships don't always win wars. Snubs actually play them. BSs are just support. I just didn't memorize snub numbers due to sheer number size, but they are mostly proportional to battleship numbers. By that, and with knowledge that Bretonians are making dozens of Templars and Challingers every day, what is higher than most factions, I would put them a little bit higher.
I don't know the accurate number of battleships for every faction. Just for Bretona and Gallia - I did a rough evaluation by knowledge that Kusari had enough battleships, before Gallia came, to make Bretonians retreat and that Rheinland had about the same amount as they did. Liberty had almost twice more of BSs than Rheinland. The whole evaluation depends on the size of the Bretonian garrison.
If a Sirius wide war happens, all Houses would wound each other badly. The side who would win will be in a desolate part of Sirius, far from any great power. They would just come to finish the others off.