  In the three-Higgs doublet model (3HDM) frame, we search for discrete flavour
symmetries that give relations among the lepton masses and their mixing angles.
We explore discreet non-Abelian groups of order less than 1035, treating
neutrinos as Majorana or Dirac particles. Despite the free dynamic parameters
available in the model, none of the groups fully predicts the lepton data.
However, some of the scanned groups provide either the correct neutrino masses
and mixing angles or the correct masses of the charged leptons. $\Delta(96)$ is
the smallest group compatible with the experimental data of neutrino masses and
PMNS mixing. $S_4$ is an approximate symmetry of Dirac neutrino mixing, with
parameters staying about $3\sigma$ apart from the measured $\theta_{12}$,
$\theta_{23}$, $\theta_{13}$.
