  Classification of differential-difference equation of the form
$\ddot{u}_{nm}=F_{nm}\big(t, \{u_{pq}\}|_{(p,q)\in \Gamma}\big)$ are considered
according to their Lie point symmetry groups. The set $\Gamma$ represents the
point $(n,m)$ and its six nearest neighbors in a two-dimensional triangular
lattice. It is shown that the symmetry group can be at most 12-dimensional for
abelian symmetry algebras and 13-dimensional for nonsolvable symmetry algebras.
