Non-Abelian Discrete Flavor Symmetries on Orbifolds

We study non-Abelian flavor symmetries on orbifolds, $S^1\mathrm{/}{Z}_2$ and $T^2\mathrm{/}{Z}_3$. Our extra dimensional models realize $D_N$, $\mathrm{\Sigma }(2N^2)$, $\mathrm{\Delta }(3N^2)$ and $\mathrm{\Delta }(6N^2)$ including $A_4$ and $S_4$. In addition, one can also realize their subgroups such as $Q_N$, $T_7$, etc. The $S_3$ flavor symmetry can be realized on both $S^1\mathrm{/}{Z}_2$ and $T^2\mathrm{/}{Z}_3$ orbifolds.