Their plan was to assassinate Uriel Septim VII, who was to visit Morrowind at the time, and install one of his sons on the throne instead, believing as they did that "The blood of the Septims runs thicker in his sons".
General Darius, the Imperial Legion commander, is aware that there is such a plot. However, and tasks the Nerevarine to track down this threat and stop it, which the Nerevarine subsequently does. The only known members of this cult (to date) are those members, and as they only appear in the one mission in the game. They are not a joinable faction.