Well, there's about half a dozen factions within the Fog in the manga, if you've read it
First off, the main Fog faction, lead by the Supreme Flagship, Yamato, who wants the Fog to learn what it means to be human; her intentions are as yet unknown
Then there's the Scarlet Fleet, commanded by Yamato's sister Musashi; they have some humans on their ships, and has recently begun meddling in human matters for reasons that are, once more, unclear
Then there are the 'Rebel' factions; one is lead by Hood, who is opposing the Scarlet Fleet's involvement in human affairs.
Then there are the 'Rogue' ships like Repulse, Haruna, Kirishima and Maya, who are off doing their own thing.
And finally, we have Blue Steel, the protaganists of the manga, centered around I-401, Takao, Hyuuga and one or two human boats.