The Middle
The Middle is one of the Five Fingers, the five most powerful Syndicates in the City holding enough power to rival the Wings. It is not involved in the war for Nest L and does not make a direct appearance in Library of Ruina, due to being weakened before the story began by The Black Silence. However, a former member does make an appearance as one of the members of The Reverberation Ensemble.
The Middle also appears in the fifth chapter of Limbus Company within U Corp, where they control the Twinhook Pirates as a subsidary. It is established that there is a ranking system of "Big Siblings" and "Little Siblings". It is strongly emphasized that The Middle "Never Forgets", making them an extremely vengeful faction. Members often keep a rulebook on them to accurately punish their foes depending on what rule was broken.
See Also
The Middle - Limbus Company Wiki