conspiracy has 2 distinct synonyms spread across 3 of its 3 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.
a secret agreement between two or more people to perform an unlawful act
a plot to carry out some harmful or illegal act (especially a political plot)
a group of conspirators banded together to achieve some harmful or illegal purpose
Synonyms, antonyms and the broader and narrower relations for conspiracy come from Princeton University’s WordNet. Full sources and licences.