  We construct an $SU(3)_L \times U(1)_N$ gauge model based on an $S_{2L}$
permutation symmetry for left-handed $\mu$ and $\tau$ families, which provides
the almost maximal atmospheric neutrino mixing and the large solar neutrino
mixing of the LMA type. Neutrinos acquire one-loop radiative masses induced by
the radiative mechanism of the Zee type as well as tree level masses induced by
the type II seesaw mechanism utilizing interactions of lepton triplets with an
SU(3)-sextet scalar. The atmospheric neutrino mixing controlled by the
tree-level and radiative masses turns out to be almost maximal owing to the
presence of $S_{2L}$ supplemented by a $Z_4$ discrete symmetry. These
symmetries ensure the almost equality between the $\nu_e$-$\nu_\mu$ and
$\nu_e$-$\nu_\tau$ radiative masses dominated by contributions from heavy
leptons contained in the third members of lepton triplets, whose Yukawa
interactions conserve $S_{2L}$, even after the spontaneous breaking. The solar
neutrino mixing controlled by radiative masses including a $\nu_\mu$-$\nu_\tau$
mass, which are taken to be the similar order, turns out to be described by
large solar neutrino mixing angles.
