Here is a ship and population breakdown for the Colonial remnant in this story.
Military Ships
Missilestar Orion
Gunstar Shaitan
Faststar Lamia (Manticore III Variant)
Battlestar Apis (Osiris II Stealthstar Variant)
Escortstar Aphid
Patrolstar Vigilant
There are also 10 Raptors (6 Stealth and 4 Standard variants 2 CSB and 2 Colonial Navy) that are not ships but important and useful assets.
These above are listed in combat potential only.
CIF/Auxiliary
Zephyr
Sandpiper
Repairstar Sarek (Vulcan Variant)
Botanical Garden Ship Dykstra
3 other ships converted to hydroponics to keep the fleet supplied in food.
One Tyleum Processing ship
6 mining ships including the Lucky Zenith which is part of the CIF.
Passenger Ships
La Bellot
Pallas
Grand Adour
Cargo Ships
Joshua
Ruth
Coral
Jetty
Yark
Indri
Total 55 ships 6 military 47 civilian and 2 "Auxiliary" The 26 non mentioned ships are passenger, cargo, or whatever standard ships. Like the Fugitive Fleet on BSG. The writers only named like half of the ships of the Fugitive Fleet and even then a lot was of the "Baltar got 789 votes" more than "what is this ships purpose in this fleet."
Population
Orion's fleet 3803
Lamia's fleet 1758
Apis' fleet 10215
Total 15,776