  We investigate the indicators for certain groups of the form $\BZ_k\rtimes
D_l$ and their doubles, where $D_l$ is the dihedral group of order $2l$. We
subsequently obtain an infinite family of totally orthogonal, completely real
groups which are generated by involutions, and whose doubles admit modules with
second indicator of -1. This provides us with answers to several questions
concerning the doubles of totally orthogonal finite groups.
