  We show that a large number of $CY_3$ manifolds are involved in an intricate
way in Mathieu moonshine viz. their Gromov--Witten invariants are related to
the expansion coefficients of the twined/ twisted--twined elliptic genera of
$K3$. We use the string duality between CHL orbifolds of heterotic string
theory on $K3 \times T^2$ and type IIA string theory on $CY_3$ manifolds to
explicitly show this connection. We then work out two concrete examples where
we exactly match the expansion coefficients on both sides of the duality.
