I'm going primarily off memory, but I'd say that's pretty darn accurate to what I recall.
Apropos of nothing in your diagram, it's maybe worth mentioning that these should be seen as stereotypes and loose interpretations unless your campaign is focused on these inter-relationships. I found it very easy to swing big in either direction -- either ignoring these connections to the point that some Factions became pretty samey, or stressing them so hard that the players would sometimes draw annoyingly erroneous conclusions (as opposed to wrong-but-fun ones). So, it's worth noting that there can be gradients and degrees in all of this stuff.