On proulx's four exceptional toroidal groups

V. K. Proulx has proved that every finite group having a Cayley graph embeddable in the torus is, with four unresolved exceptions, a quotient of a Euclidean space group. It was conjectured that these four unresolved groups are not exceptional, that they in fact are Euclidean space-group quotients. It is shown here that one is not exceptional, but the other three are.