Scarlet Brotherhood
The Scarlet Brotherhood are an evil faction from the Greyhawk setting of Dungeons & Dragons, who rule over the mysterious southern nation of Shar - not to be confused withr Shar, the Goddess of Darkness and Despair from the Forgotten Realms. The Brotherhood can be basically summed up as D&D Nazis. If the Nazis were more into enslaving all other sapient races and using magic and alchemy to perform unnatural crossbreeding experiments between humanoids, monsters and animals to engineer superior slave-creatures than genocide. Originating from a Ku Klux Klan-like society dedicated to the "protection, preservation and purification of Suel culture and blood", the Brotherhood miraculously survived the Rain of Colorless Fire that destroyed the ancient Suel Imperium because their founder, one Kevelli Mauk, happened to have possession of Lendor's Matrix, an hourglass-shaped artifact that can stop time and transport groups of people over vast distances.
They were fleshed out in a boxed set, called, simply, the Scarlet Brotherhood. This also reintroduced the Assassin class, which had been left out of the 2nd edition Advanced Dungeons & Dragons Player's Handbook, a variant Monk, and Specialty Priests for the Suloise pantheon.
Hierarchy
The Brotherhood, on paper, has a class-based hierarchy, where three specific classes hold all of the power; Monks at the pinnacle, Assassins in the middle, and Thieves at the bottom. Warriors, Priests and Wizards have no official place in the hierarchy, though they may be extended temporary power usually equivalent to the Assassin on the totem pole. In practice, bureaucracy muddles the issue.
Factions
Although the Brotherhood has a singular goal - total Suloise domination of the world - they're divided into all kinds of different factions. Some of these are based on different methods of pursuing the Brotherhood's goal, whilst others are more concerned with political power within the brotherhood.
The Bankers advocate the pursuit of financial domination, arguing that economic strangleholds and subversion can choke other nations and races into bowing their heads to Suel masters without the messy need of fighting.
The Brass Daggers are a political movement within the Brotherhood, consisting of Deathseekers (priests of Pyremius) who wish to claim domination over the Scarlet Brotherhood and make it into an extension of their church.
The Brotherhood Arcane is an alliance of Brotherhood wizards who are annoyed at the fact that despite all they do for the Brotherhood, they have no official place in its hierarchy, and demand they be given their proper respect.
The Cabal of the Everburning Flame is a small sect of Wee Jas-worshipping fire elementalists who seek to promote the worship of the Goddess of Death and Magic. Because of this, they have a strong political alliance to both the Brotherhood Arcane and to the Eyes of the Stern Lady, discussed below.
The Eyes of the Stern Lady are Wee Jas worshippers (2/3rds clerics, 1/3rd wizards) who enforce obedience to the Brotherhood's laws, whilst also seeking to promote the power and influence of their goddess within the ranks of the Brotherhood.
The Fangs are a band of warriors and priests of Llerg, and are essentially a splinter-sect of the Strong Hand that wants to grant warriors and priests an official place amongst the Brotherhood's leadership. It's extremely rare that they are not allied with the Strong Hands.
The Farseekers want the Brotherhood to temporarily re-prioritize their goals, switching their focus from conquest in the short-term to focusing on exploration into Flanaess, Hepmonaland and Amedio. Because of this, they oppose the Strong Hand, but are willing to align with more "subtle conquest" focused factions like the Bankers and the Redblades.
The High Unity faction thinks that the Scarlet Brotherhood maybe needs to tone down the racism a little, arguing that there are certain admirable traits to be found in other human bloodlines or things worth learning from the likes of elves and dwarves - they still feel the Suel are destined to rule, they just think that they can also learn or otherwise benefit from other races. This makes them extremely unpopular and keeps their numbers small.
The Homeland Nobility are a pathetic joke faction consisting of the surviving heirs to the remaining Suloise Noble Houses, who advocate for a return to the ancient ways of monarchy and aristocracy. Unfortunately, because basic Shar education talks quite lengthily about how the eccentricity of the past Suel emperors and the squabbling of Suloise nobles in the early days of Shar's settlement nearly destroyed the race, nobody outside of the remaining noble bloodlines bothers listening to them.
The Jade Wasps are a faction based on worshippers of Bralm who don't have a personal goal, they just support whoever looks to be taking the most active role in actually getting shit done at the moment.
The Millennialists are a dying faction who cling to a century old prophecy that a great miracle will occur that will bring about a purified and strengthened Scarlet Brotherhood. As the prophecied dates came and went without incident, people gave up on them.
The Pure Suel are a bunch of crazies so racist that they are too much for the Scarlet Brotherhood! They demand the purging of all non-Suel influence from the Brotherhood; this means the casting out of all spells not invented by Suloise wizards, the destruction of all non-Suloise-created magic items in the Brotherhood, and the abandonment of all weapons other than the traditional weapons of the Suel. This fanaticism has driven away pretty much everybody, leaving only a tiny handful of old cranks to cling to it; they're going to die out soon.
The Redblades are a faction of Pyremius-worshipping assassins who promote a greater reliance on the wide-scale use of poison to achieve the Brotherhood's goals.
The Speakers of the Black Smoke are worshippers of Syrul who have no personal beliefs of their own, but infiltrate and destabilize the other factions to prevent them from gaining too great an influence over the brotherhood as a whole.
The Strong Hand advocate active military assault and conquest to begin expanding Shar's hold over Flanaess.
The Thieves Majority are, as the name suggests, a band of thieves who are ticked off that their class is considered so low on the totem pole, despite the long-term and risky operations they undertake on the Brotherhood's behalf, and especially are annoyed that they remain so underappreciated mostly due to tradition. They oppose the ambitions of the Brotherhood Arcane because they fear that if wizards were officially added to the Brotherhood's hierarchy, it would be as superiors to the thieves.
The Truth Scourge are priests of Syrul who advocate her religious prominence within the Brotherhood and an increased reliance on secret agents and double-agents to destabilize enemy forces. Surprisingly, they are most likely to form alliances of convenience with the Redblades faction.