Heller has said that it's a Sherlock Moriarty type of set up, and as we know Moriarty isn't the head of a criminal organisation, he's more of a consultant criminal, and on several occasions Red john has been indirectly involved with other crimes in return for loyalty. So while I believe he does have a large network of friends I don't believe he is the head of any organisation, he's more of what Jane is to the CBI. Fearful symmetry indeed. 
I don't as yet have a theory as to how the Tyger club fit in to all of this, but there is definitely something connecting the two. What is the purpose of this group? Why was it set up, and by who? And what connects them to Red John meaning that they have to directly hijack any attempt by Jane, who while works with law enforcement has his own agenda, meaning that he cannot be corrupted, or his information cannot be intercepted by the Tyger club as easily as it would if the Unit was working on it above board. What are they hiding, and how is Red John involved with it?