The Hitotsubashi Faction was a political faction lead by one of the Tokugawa branch families that gives the group its name. Introduced during the Courtesan of a Nation Arc, they will become one of the main antagonists starting from the Shinigami Arc.
At the end of the decade long Joui Wars, a general from the Hitotsubashi family lost a battle against the rebels. This caused the family to lose their political standing despite the government winning the war. In retaliation, the family conducted a purge against the rebels that participated in the battle and those associated with them. The family, lead by Nari Nari, spent the next ten years trying to regain their standing and gathering allies while trying to dodge assassination attempts from their powerful political rival and distant relative, Tokugawa Sada Sada. Meanwhile, Nari Nari's son, Nobu Nobu, was groomed to be the next Shogun after Sada Sada placed his nephew, Tokugawa Shige Shige on the throne. Their wish was to make Japan a superpower so as not to rely on other powers, like for example, the Amanto.
A serial killer targeted Hitotsubashi officials and one of the faction's allies, the Mimawarigumi, watched the prime suspects, the Tokugawa Faction (Sada Sada was behind the murders). Thanks to an independent series of events that mainly stemmed from Sada Sada's past illegal dealings coming back to haunt him, Shige Shige resigned as Shogun so that Sada Sada can be charged without the protection of the government. Sada Sada was then assassinated by another of the faction's allies, Takasugi Shinsuke, before Sada Sada's own allies, the Tenshouin Naraku and the Tendoushuu could save him. The Tendoushuu decided to reinstate Shige Shige as Shogun as a buffer to stop the Hitotsubashi, yet with the real barrier, Sada Sada, out the way, they believed they were one step closer to being in charge.