  The use of nonabelian discrete groups G as family symmetries is discussed in
detail. Out of all such groups up to order g = 31, the most appealing
candidates are two subgroups of SU(2): the dicyclic [double dihedral] group G =
$Q_6 ={ }^{(d)}D_3$ ( g = 12 ) and the double tetrahedral group $^{(d)}T =
Q_4\tilde{\times}Z_3$ ( g = 24 ). Both can allow a hierarchy $t > b, \tau > c >
s, \mu > u, d, e$. The top quark is uniquely allowed to have a G symmetric
mass. Sequential breaking of G and radiative corrections give the smaller
masses. Anomaly freedom for gauging $G \subset SU(2)$ is a strong constraint in
assignment of fermions to representations of G.
