the original Deus Ex: when I was a kid I figured the usual stuff about people with different affiliations as rather one big blob with their associations, but the sub faction of majestic 12 within the illuminati taught me how group associations aren't a singular collective blob, but sub-factions within sub-factions down to even the individual level that have their own interest that working with relatively like minded people helps to get or at least to get something close enough to compromise.
The greatest mistake you can make in groupings is thinking them as a collective blob, instead of understanding they are individuals who happen to share something as an notable trait but they are not that singular trait. even if you were to withness some sort of illuminauti meeting, while they'd have things that make them a part of that group, philosophically, culturally, etc.
They still have meetings to discuss things because they'd have internal arguments over things, if groups were to completely agree with each other 100% of the time, then having meetings and conventions would be pointless. It made real world politics easier to understand when a broad political "group" seems to do contradictory actions, because of sub groups or even just individuals in the same "faction" not agreeing with how something is done, either going too slow, too fast, or wanting a different action entirely done.