No offense, but the Triads are maybe a distant third.
That's just what they WANT You to think.
No, not really. See, what the two big OC groups in Shadowrun (and let me emphasize that:
in Shadowrun) have in common with each other is something that the low-level groups simply
don't - a capacity, a capability, to be flexible in regards to the people with whom they work, and of whom they accept into their midst. Ask yourself what it would take to get someone into your Group Of Choice. Both the Mafia and the Yakuza will give pretty much
anyone work for years, allow you to be their gopher. If you prove your loyalty again and again and again (and again times about a zillion, but still), you can get made. Would it be easy? Oh, hell no. But it would be
possible, eventually.
The Mafia of SR is composed of the original Sicilians,
and the Irish,
and the French,
and the Algerians,
and the Greeks,
and a whole bunch of others who were never Italian in the first place. The Yakuza in SR may not
currently include rengo of Koreans, or Native Americans, or etc., but they are in many ways (and in many places) slowly evolving the 'we don't accept nobody who ain't one of us already' thing into something that
does permit The Other to become one of them, so long as The Other is loyal unto and beyond death.
Almost all, if not
actually all, of the other crime groups are self-isolationist. They recruit and accept members from their own kind - Grey Wolves, Koshari, Seoulpa Rings, Vory v Zakone and the Triads as well. (Yes, I know that depending on the specific leader, the definition of 'our own kind' can sometimes be flexible, but it begins and ends
with that leader. And yes, I know that the Vory and the Triads are counted as 'major' by the Vice book, etc. but neither has the sort of penetration that the Yaks or the Mob do.)
Another point is, simply, the level of violence intrinsic to their operations. The Mob and the Yaks can pull out the stops - and for them, those can be really
big fraggin' stops. But they don't revert to it immediately the way the other, smaller,
younger syndicates do. It is in part because of size, but it's also because of maturity and societal penetration. They focus less on overt violence - which gives tremendous leverage for a short period of time - and more on influence acquired by other means (financial, legal, whatever), which is leverage writ large and long. Any expansion of a smaller group outside of their personal zone in a major international-level sprawl like Seattle - Chinatown, a NAN enclave, the Russian zone - leads to that quiet influence being applied simultaneously with defensive stuff. Why put your head out where it can be blown off - or raise your profile so that the citizenry calls for your elimination - when you can simply nudge a councilman or two to get a block rezoned, buy out and demolish a warehouse, or refocus KE's attention on the upswing in violence in the target area?
The Triads remain violent. Their members can't even be
questioned at length, which isolates them. And then there's the question of whether they see the civilians as protectees or prey ...