  In this work, we study the phenomenology of neutrinos and the formation of
cosmic domain walls in the NMSSM extended by an $A_4 \times Z_3$ flavor
symmetry. Neutrino masses result from the type I seesaw mechanism using only
two flavon fields and the NMSSM singlet $\mathcal{S}$ while their mixing is of
Trimaximal mixing form. We perform our phenomenological study in the normal
mass hierarchy where we find that observables like $m_{\beta\beta}$, $m_\beta$,
and $\sum_i m_i$ can be tested by future experiments. Due to the difference
between the $A_4$ subgroups that undergo spontaneous breaking in both the
charged lepton and neutrino sectors, the resulting domain walls in each sector
exhibit distinct structures. We delve into the details of the breaking patterns
within these two sectors, and we introduce a nuanced geometric representation
for them. To tackle the domain wall problem, we explore a well-established
method involving the explicit breaking of the flavor symmetry. This is achieved
through the introduction of Planck-suppressed operators induced by
supergravity.
