In Japan there are many types of Yakuza but this story involves the arguably most influential clans. The Tojo clan is the most powerful and largest clan, the clan able to control main areas of Tokyo, obviosly that'd be most beneficial as it's a fuckin major city. The Omi Clan is pretty much a entirely separate Yakuza faction, they usually control more southern region like Osaka but are almost as powerful but usually just that sliver less than Tojo.
Within clans like Tojo, I forget the translated terms, but the Chairmen is basically the King, the #1 decision maker and powerholder, all the power holders usually have their own families as well. Then after that are family patriarchs, this is like the Dojima family which is basically the most powerful singular family in the Tojo due to manpower and revenue production, these main families are like the limbs of the chairman, while those families can have their own captains within them as well that have their own families, acting like the fingers and ect. Suhei Dojima's family also has Kazama Shintaro as his captain under him, which in turn has the Kazama family under him. It gets kind of blurry but that's the gist of it.
Sagawa is a part of the Omi Clan and your involvement from him comes from the fact that Tojo clan Patriarch Futoshi Shimano is exiling you and pulled a favor for Sagawa to leash him for Shimano. This only happened because of a type of alliance of Sagawa and Shimano being brothers, not in the literal sense but in the Yakuza being "Sworn brothers" means you are basically comrades of war and basically live and die in the fire together.
