The Federal Coality
The Coality is a federation of interdependent governorships spanning the stellar expanse of the empire. Most (60%) are variations of a bureaucratic representative democracy template agreed to by treaty. The remainder are corporate (20%), oligarchy of some flavor or another (15%), industrial socialist (3%), utopian/religious (2%), balkanized (<1%), and creepy feudal theme park (Phoenix System). Coality governments also vary in degree of Imperial loyalty.
Federal Departments within the Coality
All Coality departments have been mandated by treaty for so long that they compete for power on their own within a population, both against the Governors and among themselves. Organized independently in a rigid (some say ossified) hierarchy. Corruption is a constant problem.
Assembly of Planetary Governors
The lawful governments of populations that comprise the body politic of the Coality. So named because Governorships usually control planet-level volume or population, but some are as small as city-states or outpost habitats (e.g. new colonies, naval bases with high permanent residence, corporate grants). Many span whole systems. Governorships are awarded exclusively by the Imperium, in exchange for capital tax (or levy, tithe, rent, services rendered, whathaveyou). Although the APG is a civic body, the higher-level executives tend to be members of the peerage (Governors, e.g. are 75% noble, from landed peers all the way up to royalty).
Parliament of the Coality
Formal liaison to the Imperium. Parliamentary appointments by the Assembly. Parliament is charged with providing direction to, oversight for, and communication among Coality departments. The actual power of the Parliament varies widely with the individual Parliamentarians. Some have power and influence, many more are in roles that are largely ceremonial.
Commerce, Trade, and Standards
Regulators of private enterprise, trade, banks, and credit (money). Organized internally as "Guilds" of independent corporations, unions, and merchants aligned by business domain. Like the APG, nobility is seen among the higher levels of the CTS -- especially high in instances of unlanded peerages. The Board of Directors is led by the firm hand of the Emperor's uncle (Ducal).
Federated Armies of the Coality
Planetary and in-system military, military police, intelligence. The FA has very little intersystem power. Each governorship is given latitude on the Army's organization, strength, and doctrine, and acts as its civil executive. Funded by APG as well as by the Imperium. At the highest level, FA career leaders are attached to the Imperial Navy's Security and Intelligence Council, War Council, etc.
Federal Scout Service
Intersystem communication, space travel security, exploration, and alien relations. Responsible for mapping, postal service, X-Boats, library, and media. Because by law civic governorships are not allowed to span multiple systems, the FSS raison d'etre is continuity across systems (its competitors, the Imperial Navy and interstellar Guilds, have more explicit strings attached). Mostly funded by its services.
Federal Petitionary Court
Civilian court of appeals, arbiters of the APG law. Funded by the Magistrates.