  We have performed a comprehensive analysis of the type D group $D^{(1)}_{9n,
3n}$ as flavor symmetry and the generalized CP symmetry. All possible residual
symmetries and their consequences for the prediction of the mixing parameters
are studied. We find that only one type of mixing pattern is able to
accommodate the measured values of the mixing angles in both "direct" and
"variant of semidirect" approaches, and four types of mixing patterns are
phenomenologically viable in the "semidirect" approach. The admissible values
of the mixing angles as well as CP violating phases are studied in detail for
each case. It is remarkable that the first two smallest $D^{(1)}_{9n,3n}$
groups with $n=1, 2$ can fits the experimental data very well. The
phenomenological predictions for neutrinoless double beta decay are discussed.
