Namor Deep Six
At the time of their formation, the Deep Six were purposed with the location of Namor. Namor was wanted for crimes against the surface world and had dropped off the radar. Gathering together in their base of Aquaria, they scoured the Oceans. Stingray originally named the group Deep Six, something that Tiger Shark disagreed with.
The Deep Six eventually located Namor, who was involved in a battle with the Avengers. The battle was joined by the six heroes, and eventually Crystal managed to break up the battle. Namor ended up subduing the combatants on both sides, which ended with Tamara Rahn and Tiger Shark leaving from Anger.
The group would stay together for the most part, with Stingray, Triton and Andromeda helping Namor battle the Abomination, Bloodwraith and Morgan Le Fey. However, they would lose the name Deep Six.
Attuma Deep Six
Years later Attuma, hoping to conquer Atlantis, created his own version of Deep Six, consisting of Atlantean criminal’s including: Nagala, Piranha, Orka, Sea Urchin and Tiger Shark.
Namor and the Defenders traveled to the outskirts of the nation of Atlantis, they were attacked by the Deep Six and Attuma's Army. However, before it could come into conflict, the Defenders escape, because they needed to create a strategy first.
A few days later, the Defenders led another charge on Atlantis. This time, the heroes utilized a strategy of keeping, the two most powerful members of Deep Six - Attuma and Nagala busy, while the other team members could be defeated much more easily. Hulk refused to follow the plan and confronted Orka alone, but the rest of the team followed orders, eventually relatively easily defeated him, Piranha, Sea Urichin and Tiger Shark as well. Nagala was left, but she eventually got knocked out by the Silver Surfer. Namor took care of Attuma and beat him in single contact. After this defeat, the Deep Six apparently be resolved.
Namor Deep Six was created by Glen Herdling and Geof Isherwood in 1995 and first appeared in Namor The Sub-Mariner #58.
Attuma Deep Six was created by Kurt Busiek, Erik Larsen and Sal Buscema in 2001 and first appeared in Defendrs #7.