brotherhood has 6 distinct synonyms spread across 2 of its 4 senses. Each sense below keeps its own list, because a synonym belongs to a meaning and not to a word: swapping one sense's substitute into another sense's sentence is how a thesaurus makes writing worse. WordNet records no antonym for it — antonymy is a relation between word forms rather than concepts, so it is deliberately sparse.
Counts are distinct word forms across every sense. A synonym that appears under three senses is counted once here and shown three times below, under each sense it belongs to.
the kinship relation between a male offspring and the siblings
people engaged in a particular occupation
“the medical fraternity”
the feeling that men should treat one another like brothers
an organization of employees formed to bargain with the employer
“you have to join the union in order to get a job”
Synonyms, antonyms and the broader and narrower relations for brotherhood come from Princeton University’s WordNet. Full sources and licences.