  We compute a twisted index for an orbifold theory when the twist generating
group does not commute with the orbifold group. The twisted index requires the
theory to be defined on moduli spaces that are compatible with the twist. This
is carried out for CHL models at special points in the moduli space where they
admit dihedral symmetries. The commutator subgroup of the dihedral groups are
cyclic groups that are used to construct the CHL orbifolds. The residual
reflection symmetry is chosen to act as a `twist' on the partition function.
The reflection symmetries do not commute with the orbifolding group and hence
we refer to this as a non-commuting twist. We count the degeneracy of half-BPS
states using the twisted partition function and find that the contribution
comes mainly from the untwisted sector. We show that the generating function
for these twisted BPS states are related to the Mathieu group M_{24}.
