Here's some ideas that I made decidedly not organization based since you said you wanted to be a faction likely with a foundng race attached. I tried making them all interstellar and possibly open to having a history of interacting with others. Remember the current state of your faction doesn't have to be the state it was always in and when you make a species there should be some level of diaspora.

-A society of hyper industrialists with lots of machine slaves

-A caste-based communal society that likes being regional

-A slowly expanding, ancient society that is very regimental and order based

-A large expansive, darwinistic society that is loosely controlled and has perpetual internal conflict as part of some bizarre system [I made a civ like this once]

-Upstart federation or unitary government that has recently started expanding rapidly

-A society that pretends to be technologically weak on the surface but has underground cities, some nasty defensive WMDs and a secret underground network of 
wormholes that connect their worlds.

-A large hierarchal multispecies empire that is godless.

The list I made probably only scratches the surface of possibilities, and mind all the above in my list don't necessary have to be composed of species you make. Mind the diaspora.