They operated on a ship and the members sit on top of a pillar.
When the 13th Shogun Tokugawa Sada Sada welcomed Amanto to Edo, Samurai around the country were against this and a long civil war known as the Joui War lasted for 20 years. The Tendoshu helped organised the Kansei Purge with the Bafuku, this created a friendly alliance between the two.
Besides from Tokugawa Sada Sada, they also control higher ranking officials as puppets.
They operated an underground arena called Rengokukan where they placed illegal gambling on mortal combat. Oshou Doushin also known as Kidomaru was the king of the arena.
They also run a Tensho sect and Naraku. After the Oniwabanshuu disbandment because of Jiraia failed assassination to the 13th Shogun, Sada Sada would replace Oniwabanshuu for Naraku in order to strengthen the bond with Tendoshu. But this was only to keep surveillance on the government.
They control an underground arena called Rengokukan, the Shinsengumi and Yorozuya put an end of the arena.
After the incident, Matsudaira Katakuriko and Kondo Isao were summoned to answer for the incident but only giving them a last warning.
Ikkoku Keisei Arc
The Tendoshu ship landed on top of the Shogun castle, originally they came to save Tokugawa Sada Sada but the current shogun Tokugaw Shige Shige confronted his uncle to answer for his crime. Oboro confirmed to the Tendoshu that their true enemies are Yoshida Shouyou's students.