  We consider the Berglund-H\"ubsch-Henningson-Takahashi duality of
Landau-Ginzburg orbifolds with a symmetry group generated by some diagonal
symmetries and some permutations of variables. We study the orbifold Euler
characteristics, the orbifold zeta functions and the orbifold E-functions of
such dual pairs. We conjecture that we get a mirror symmetry between these
invariants even on each level, where we call level the conjugacy class of a
permutation. We support this conjecture by giving partial results for each of
these invariants.
