  We obtain predictions of lepton mixing parameters for direct models based on
Delta(6n^2) family symmetry groups for arbitrarily large n in which the full
Klein symmetry is identified as a subgroup of the family symmetry. After
reviewing and developing the group theory associated with Delta(6n^2), we find
many new candidates for large n able to yield reactor angle predictions within
3 sigma of recent global fits. We show that such Delta(6n^2) models with
Majorana neutrinos predict trimaximal mixing with reactor angle theta_{13}
fixed up to a discrete choice, an oscillation phase of either zero or pi and
the atmospheric angle sum rules theta_{23}=45 degrees -/+ theta_{13}/sqrt{2},
respectively, which are consistent with recent global fits and will be tested
in the near future.
