Is it possible to join one of the Sub-Factions?

No; right now, the faction you chose at the start of the game, when you created your character, is your faction. That being stated, it is possible to increase your standing with any of the individual sub-factions all the way up to "Pillar Of Society" while having very poor standing with one's own faction. This may be why some players feel more identified with a particular sub-faction, group of factions, or none at all, than with the faction they chose at the game's beginning.

All of this may be subject to change, of course. The way the game is designed, faction standing counts for just as much if not more than titular faction in most cases. It will affect what equipment is offered for sale, what missions are available, whether or not that faction reacts to your presence, and how that faction penalizes others that harm you (possibly other things as well; it may affect commodity prices and/or repair prices, but I'm not certain on this).

The one time I can think of after the game's beginning where you "join" a particular sub-faction in a meaningful way (such as in a rite-of-passage, irreversible manner) is after Combat license 3 when you have the option of joining a national military.

There are or were some guilds that were allied to sub factions (albeit through RP)