Argo's own article covers its eighteenth-century division into Carina, Puppis and Vela in detail. Set aside from that later history, the whole ship also belonged, for as long as it existed as a single figure, to a much older grouping that had nothing to do with Jason's quest at all.
The stretch of sky running from Aquarius and Capricornus through Piscis Austrinus, Eridanus, Delphinus and Equuleus carries a persistent watery theme older than Greek myth-making, inherited by Greek astronomers from Babylonian sky-lore because the Sun crossed this region during the ancient Near East's rainy season. A ship afloat in a sea is the most literal possible member of that theme: unlike Equuleus, whose presence here looks incidental, Argo's presence is thematically exact, a vessel placed in precisely the stretch of sky already read as an ocean before anyone had attached the Argonauts to it.
Historians of astronomy label this loose cluster the Heavenly Waters, a modern convenience rather than a boundary Ptolemy drew in the Almagest, where his forty-eight are sorted only into zodiacal, northern and southern lists with no named thematic groups at all.
Argo was, by size alone, the largest single member the ancient sea ever held, and its eventual division was as much a practical response to an unmanageable figure as it was the end of a ship that had, for a very long time, simply been floating where a ship belonged.