<p>That's an interesting idea, but I doubt that, ethnically-divided gangs don't really tend to form out of 1 big supergang that broke apart. They form individually, based on the group's own particular history & perceived needs.
</p><p>For example, the Italian mafia formed out of alliances between the newly unified government & vigilante clans that existed previously, while the Irish mob is a much more recent organization that formed in America in response to threats from anti-Irish groups.
</p><p>In my opinion, given his belief in the innate superiority of bloodbenders & apparent ties with the Water Tribe, Yakone probably headed the Red Monsoons, maybe even the earliest incarnation of the group. It likely formed either from prisoners released from the Fire Nation & compensated or from struggles with other gangs. The Agni Kais probably arose out of anti-firebender sentiment. The Triple Threats, not being ethnically divided, would have formed for business reasons. The Terra Triad were likely either a nationalist group, perhaps descended from or based on Hundred Year War resistance fighters, or formed for business reasons.
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