SWORD is the Marine Headquarters Secret Special Force. The only known members are Koby and Drake.
From 592 cover, Akainu could also be a member.
Most likely, Sengoku and Corazon were also SWORD members at some point of time. What all these marines have in common is a strong sense of duty and justice.
Aokiji, based on his pre-TS appearances, was a very forgiving and laid-back guy who enjoyed cycling and napping more than anything.
Aokiji and Akainu faced off in Punk Hazard for 10 days. Aokiji saw Akainu as excessively cruel and detrimental to the Marine’s cause of preserving peace. Akainu saw Aokiji as too soft and lazy to put an end to evil.
I think what happened at the end of that brutal fight was Akainu came to realize Aokiji’s sense of duty and justice which was contrary to his usual demeanor. Seeing him ready to die for his beliefs earned him Akainu’s respect, which is why he didn’t kill him. Instead he chose to recruit him in his secret special service, SWORD and give him the most dangerous mission, infiltrate Blackbeard Pirates.
I think this is further proof of their hidden association.
Akainu asks the Gorosei to ignore Aokiji’s actions so that he may continue his mission. We have already seen how he went after Luffy despite having completed his mission and how he destroyed an entire ship full of children in Ohara. If Aokiji just decided to go rogue, there is no way Akainu would let him roam free and sully the name of the Marines.
*Theory by pice0fshit