Elucidated Brethren of the Ebon Night
One of the many secret brotherhoods in Ankh-Morpork, led by the Supreme Grand Master. The Brethren summoned a dragon into Ankh-Morpork to overthrow the Patrician and restore the monarchy - they had picked their own monarch, of course.
A circle of honest seekers after mystic truth whose misfortune it was to let Lupine Wonse run the group. A Supreme Grand Master with an agenda of his own is always going to be bad news in a secret society.
Had the full-time professionals in the Orders of Wizardry divined their existence, the reaction is likely to have been the same good-natured derision in which the professionals in any trade hold their under-resourced and time-poor part time cousins - ie, the way regular soldiers view Territorials, or full-time policemen look down on Special Constables. However, as the Librarian is one of the Specials in the Ankh-Morpork City Watch, the derogatory term "hobby bobby" must belong to the same lexicon as the m-word, and is not spoken by wise Watchmen. Even the brothers initially had their doubts (I don't mess with the ineffable wossnames and they don't do any plastering...).
Brother Fingers, however, gave Unseen University a reason to adopt an attitude other than amused condescension, when he stole a potent grimoire from the Library (indirectly the reason why the Librarian signed on as a Special).
Were the days of the Brethren not already numbered by Wonse's ulterior motives re. The Summoning of Dragons, it is clear that the University, in the form of the Librarian, would have taken formal or informal action of a conclusive kind once the book-theft was traced... not to mention any sanction the Thieves' Guild might have applied, for (a) unlicensed theft; or (b), if it considered any official complaint from the Wizards (or indeed, any pointed comment from the Patrician) should be passed on to the culprit with added emphasis, and possibly the stapling together of both knees.
The way this plan went wrong is described in Guards! Guards!.
The Supreme Grand Master was in fact Lord Vetinari's secretary, Lupine Wonse; Brother Fingers was identified later as Bengy "Lightfoot" Boggis. The names of the other members are unknown; their secret names were:
The group's name appears to be a reference to the real-world magical society, Hermetic Order of the Golden Dawn.