I thought I'd post this graphic (below) as a visual reference to show part of the behind the scenes process involved in developing a faction logo for games (or anything really). In this case the logo in question is for the Nanomei faction from Anvil Eight's board game Aetherium.
We went through a similar process many times during the creation of the original Aetherium game box. It's easy to come up with something quickly, but if time is spent and thought given to a logo like this you can develop something far better than your initial sketches might suggest.