Khanate Faction Confusion

Unmarked spoilers ahead for people who are not acquainted with the Reformer of Reputations

So once you build your network sufficiently in the Khanate, you can choose to side with a particular faction for the Pulling of a Thread: Opportunity carousel. I understand the motivations and such of the Bazaar, Surface Power, and Deep Power factions, but what about the three Khanate clans? Besides the standard manoeuvring for power, what motivates the Tortoise? Why should I, for example, side with the Eagle over the Leopard? I have close to no idea what any of them want, and that is quite risky when doing spycraft. So what are the philosophies behind the feuding factions native to the Khanate?

I’m absolutely not an expert, but I believe the idea is that each clan controls a different aspect of the Khanate’s operations. Per the lore wiki, the Leopard are the ruling clan, the Taimen control the intelligence force, the Eagle control the Navy, the Tortoise control manufacturing, and the Wolf seem to do all the actual work.