Imperial fleet during the operation against Kharak
The Taiidan Imperial Navy was the space forces of the Taiidan Empire. At the time of the Homeworld War, it fielded 137 Carriers amongst many other ships.
Overview
The Imperial Navy maintained hundreds of installations around the galaxy, including space stations that made up the Empire's heavily fortified border, and a Hyperspace Inhibitor Network that surrounded the Hiigaran System. It was also capable of fielding carrier groups far beyond the Empire's frontier. Also the Taiidan Navy is known to cooperate with the Turanic Raiders, most notably including the attack on the Kushan Mothership during the Kharakian Genocide.
Strength
The Homeworld: Cataclysm manual states that 137 Carriers were in service at the start of the Homeworld War. Using this figure a broad, if probably quite low, estimate can be deduced of the total strength of the Imperial Navy. During the Homeworld War the Mothership and her fleet encountered and defeated seven of these carriers. By comparison roughly eleven Taiidani cruisers, thirty destroyers, three hundred frigates, two hundred corvettes, four or five hundred fighters and several dozen support vessels were similarly encountered.
Extrapolating from these figures would give the Taiidani Navy a strength of 215 cruisers, 600 destroyers, 6000 frigates, 4000 corvettes, as many as 10,000 fighters and perhaps a thousand major support vessels (resource collectors, cloak generators etc). This estimate actually seems very low given the context. The manual also stated that the Taiidan Empire at the time ruled 150 star systems and 360 billion people spread out across a significant fraction (maybe as much as half) of the populated galaxy. Its possible that other kinds of Taiidani Carriers were in service at the time. Little canonical information has ever been given about the nature of spacecraft and space stations in the Homeworld universe beyond military vessels. It is stated that the number of Taiidani citizens living in space-based colonies numbered at least 'in the millions'. However only a handful of Mothership Class Taiidani vessels were seen in-game, including the Emperor's Flagship in the final level, the Supernova Research Station in level 10 and possibly the few Taiidan 'outposts' seen in the cutscene before level 6.
In the cutscene before level 14 of Homeworld, an image is shown of the hyperspace inhibitor network surrounding Hiigara. There appear to be thirty-nine inhibitors shown and the Mothership fleet has been directed to the 'most vulnerable inhibitor station'. Given that the inhibitor attacked is protected by a massive sphere of about 150 ion cannon frigates, as well as a heavy cruiser, several destroyers, a carrier and its accompanying squadrons of strike craft, the total number of ships assigned to guarding Hiigara alone must be truly mind-boggling. In fact if you do the math, it implies that about as many, if not more, ships are guarding Hiigara alone than the total estimate of the Imperial fleet's size deduced above.
History
The precursor of the Imperial Fleet was the Taiidan Navy, which battled with Hiigaran Empire back in 3000 BHL. After the devastating Hiigaran strike on the Taiidan Homeworld, Admiral Riesstiu gathered the remains of the Taiidan Navy and struck back at the Hiigaran Empire, conquering or annihilating hundreds of worlds. Taiidan military action, coupled with the Hiigaran fleet being shattered after battling the Bentusi, eventually lead to the Hiigaran Exile, and the establishment of the new Taiidan capital on Hiigara.
Admiral Riesstiu would later become the first Taiidani Emperor, and the Taiidan Navy renamed to the Taiidan Imperial Navy.
Rebellion and the end of the Imperial Fleet
By the time of the Homeworld War, the Imperial Fleet had grown enormous both in size and expense, due mainly to the last emperor's increasing paranoia. Grumbles spread across the Empire, and factions moved to plant the seeds of insurrection against their insane emperor. The Kharakian Genocide, meant to solidify Imperial power, was met almost universally by revulsion, and provided the spark that triggered the inevitable rebellion. In response to the uprising, the Emperor declared martial-law on all of the Taiidan worlds, and an executions of anyone standing against the empire begun across the empire. The Imperial fleet was ordered to destroy the life support systems on asteroid cities that resisted, so that the records of slow death of hundreds of people could be shown to the millions as an example.
The Battle of Vorshan's Rift nearly destroyed the Rebel fleet. However, with a stroke of luck then the Kushan Fleet was pulled out of Hyperspace and thrust into the battle, guarding group Captain Elson, one of Rebel leaders who had escaped from the battle. Elson managed to give critical information to the Kushan on the location of their homeworld, allowing them to break through the network of hyperspace inhibitors surrounding the system. Elson and the rebels formed an alliance that would eventually break through the inhibitor network and face the Imperial Fleet stationed above Hiigara itself. In the aftermath of the battle, the Imperial Fleet, along with the Emperor and his Elite Guard lay in ruins.
The remnants of the Fleet either surrendered or fled into hiding to form the Taiidan Imperialist Faction.