  Following the way proposed recently by Hernandez and Smirnov, we seek
possible residual symmetries in the quark sector with a focus on the von Dyck
groups. We begin with two extreme cases in which both $\theta_{13}$ and
$\theta_{23}$ or only $\theta_{13}$ are set to zero. Then, cases where all the
Cabibbo-Kobayashi-Maskawa parameters are allowed to take nonzero values are
explored. The $Z_7$ symmetry is favorable to realize only the Cabibbo angle. On
the other hand, larger groups are necessary in order to be consistent with all
the mixing parameters. Possibilities of embedding the obtained residual
symmetries into the $\Delta(6N^2)$ series are also briefly discussed.
