'The Umbrella Academy' Season 2: Who were the Majestic 12, was it a real organization?

Spoilers for 'The Umbrella Academy' Season 2

Netflix's fan-favorite superhero dramedy 'The Umbrella Academy' is finally back with Season 2. Set in the 1960s, the new season brings up a lot of history lessons both real and fictional, including a conspiracy theory about a secret cabal called the Majestic 12. In Episode 4 'The Majestic 12', Diego Hargreeves / Number Two / The Kraken (David Castañeda) and Number Five / The Boy (Aidan Gallagher) discover that their father Reginald Hargreeves (Colm Feore) is part of a shadow organization called the Majestic 12 that may be behind the assassination of President John F Kennedy. 

The Majestic 12 is described in the episode as a secret group of scientists, military strategists and government officials who have been controlling the United States government from the shadows for years. The organization is in fact based on a conspiracy theory popular among ufologists in the 1980s. There's a slight discrepancy here because while the organization is believed to have been started in 1952 by President Harry S Truman, the myth of the Majestic 12 only really became popular in 1984 when papers detailing the organization's secret history were circulated among conspiracy theorists. We don't know how Number Five's conspiracy nut friend would have heard about the organization in 1963 but considering all the other problems with the timeline, we're ready to let that one slide.