  Using the type-II seesaw mechanism with three Higgs doublets phi_alpha (alpha
= e, mu, tau) and four Higgs triplets, we build a model for lepton mixing based
on a 384-element horizontal symmetry group, generated by the permutation group
S_3 and by six Z_2 transformations. The charged-lepton mass matrix is diagonal;
the symmetries of the model would require all the three masses m_alpha to be
equal, but different vacuum expectation values of the phi_alpha allow the
m_alpha to split. The number of parameters in the Majorana neutrino mass matrix
m_nu depends on two options: full breaking of the permutation group S_3, or
leaving a mu--tau interchange symmetry intact; and hard or spontaneous
violation of CP. We discuss in detail the case with the minimal number of three
parameters, wherein m_nu is real, symmetric under mu--tau interchange, and has
equal diagonal elements. In that case, CP is conserved in lepton mixing,
atmospheric neutrino mixing is maximal, and theta_{13} = 0; moreover, the type
of neutrino mass spectrum and the absolute neutrino mass scale are sensitive
functions of the solar mixing angle.
