Ok, short intro: factions - private groups - squadrons
(minor) Factions: show up in game and may own certain assets (like stations). There are some minor factions that have been created on player's requests, and others that have been adopted by players or groups of players, but apart form that, there are no visible effects. Those minor factions will keep on doing what they do, whether the players care for them or not. In the latter case, people also sometimes talk about orphaned factions.
Private Group(s): a game mode, like Open or Solo. Every player can create a PG and invite other players. As long as you're playing in that PG (and on the same platform), you will ony encounter players who belong to the same PG. A PG may be as small as one player, or have 40,000 members (like the Mobius PG).
Squadron: A rather more recent way to show your allegiance to an informal group. Unlike with a PG, you need to spend a little in-game money (10 MCr, equivalent to half a VO core asteroid) to create a squadron. For that, you get your own comms channel and squadron marker in the comms panel, and the chance to compete against other squadrons at various in-game challenges. But you can only be a member of one squadron at any given time.
For the Fighter Club, you should join the PG and the Discord channel. Anything else is optional.
