The general administrative and peacekeeping force of the galaxy is The Collective. Originally comprised of humans, representatives from every intelligent species encountered so far have been added over time if the species decided they wanted to send a delegate. A species is not contacted by The Collective until they reach the stage of development of suitably advanced spacefaring technology, and it is a breach of interplanetary law to make contact with an underdeveloped species.
The main focus of The Collective is actually data collection and storage, and the administration and peacekeeping aspects came later and with less intensity. Problems that are confined to a planetary or even solar system level are generally left to the discretion of local officials, but if any issue becomes large enough to affect other solar systems then The Collective steps in to provide guidance and even force if absolutely necessary. The vast array of ships that comprise The Collective are designed to gather information about cosmic anomalies and the flora and fauna of the many planets in the galaxy first, and designed to keep the peace second. Due largely to the broadly non-interference of The Collective, most intelligent species accept their guidance and allow them free passage and free trade through their respective areas.
While The Collective is only vaguely hierarchical in most aspects, there is a small body that makes the broad overarching decisions. This small group is composed of the highest ship-level artificial intelligence that are connected to each other through near-instant communication tunnels, but still retain a degree of separation so they do not merge into one super artificial intelligence. Every ship-level artificial intelligence is aware of the existence of all of the rest of them because there are not an inordinate amount of them in the first place, and as a community they make the decision of which among them is elected to the administrative board. The location and exact number of the board is not known to the general public for security concerns, but its decisions are still accepted because it has thus far been entirely effective at whatever decision it have to make.