We consider compactification of the SO(32) heterotic string on a 6-dimensional Z 3 orbifold with one discrete Wilson line. A complete set of all possible embeddings is given, 159 in all. The unbroken subgroups of SO(32) are tabulated. The extended gauge symmetry SU(3) 3, recently discussed by Kim [ hep-th/0301177] for semi-realistic E 8× E 8 heterotic string models, occurs for several embeddings, as well as other groups that may be of interest in unified string models. The extent to which extra gauge group factors can be hidden is discussed and compared to the E 8× E 8 case. Along flat directions where an effective hidden sector exists, the embeddings described here provide for hidden gauge groups that are not possible in the E 8× E 8 heterotic string.