  We perform a detailed analysis of $\Delta (6n^2)$ family symmetry combined
with a generalised CP symmetry in the lepton sector, breaking to different
remnant symmetries $G_{\nu}$ in the neutrino and $G_{l}$ in the charged lepton
sector, together with different remnant CP symmetries in each sector. We
discuss the resulting mass and mixing predictions for $G_{\nu}=Z_2$ with
$G_{l}=K_4,Z_p,p>2$ and $G_{\nu}=K_4$ with $G_{l}=Z_2$. All cases correspond to
the preserved symmetry smaller than the full Klein symmetry, as in the
semi-direct approach, leading to predictions which depend on a single
undetermined real parameter, which mainly determines the reactor angle. We
focus on five phenomenologically allowed cases for which we present the
resulting predictions for the PMNS parameters as a function of $n$, as well as
the predictions for neutrinoless double beta decay.
