  We determine two new infinite families of Cayley graphs that admit
colour-preserving automorphisms that do not come from the group action. By
definition, this means that these Cayley graphs fail to have the CCA (Cayley
Colour Automorphism) property, and the corresponding infinite families of
groups also fail to have the CCA property. The families of groups consist of
the direct product of any dihedral group of order $2n$ where $n \ge 3$ is odd,
with either itself, or the cyclic group of order $n$. In particular, this
family of examples includes the smallest non-CCA group that had not fit into
any previous family of known non-CCA groups.
