Various factions vie for control and influence in the cluster.
The high-tech systems all have some influence or desire to influence. Mostly, Crystal 9 and New Greenland keep to themselves. New Greenland seems to spend a fair amount of time making sure Reich V (and anyone else) doesn't bother them, and the government seems to have deep intelligence on the rest of the cluster, even if they're not directly involved. Crystal 9 deliberately keeps to itself, maintaining a thin trade with other systems only, secure in the fact that it's only links are to New Greenland and Lorax. Reich V seems to dream of domination, but is hampered by their low level of technology relative to the Hive, and is stymied on the other side by New Greenland, a culture that seems more than capable of keeping them out. The Hive seems interested only in trade domination, in selling whatever they can to whoever will buy. Roanoke seems interested primarily in preventing other systems from attaining their own level of biotech sophistication; whether that's an altruistic impulse (this stuff is dangerous) or something more sinister is unknown. They don't seem to have intervened directly in the rest of the cluster in a long time (6000 years?) but they seem to be doing so now, given that they (probably?) just finished the job on Anaph that the Humming Fish started.
Somewhere in the middle are other groups. The most powerful is the sprawling Starburst Mandala Group, a subsidiary of which (Labyrinth Group) the team works for. SMG's interests are murky, but they seem mostly interested in maintaining peace or a balance of power through the cluster, and they use LG as the hammer hand to do that. It's pretty clear that SMG is the real power in the cluster, and pretty much anyone who wants to exert influence has to reckon with them. SMG seems tied to the Hive, but isn't headquartered there, and seems mostly independent of Hive politics. The other major group you know about is the Humming Fish Collective, but it's extremely hard to tell how big or dangerous they really are. The work you've seen has really been that of only 10-12 operatives. There are other groups, notably the Syndicates who operate out of Tesla, but you haven't had many dealings with them.