Normal Subgroups and Quotient Groups · Hard problem

A homomorphism $\varphi_a: \mathbb Z_{36} \to \mathbb Z_{24}$, $k \mapsto ak \bmod 24$, is well defined for certain values of $a \in \{0,\ldots,23\}$. Among exactly those valid $a$, for how many does $|\ker\varphi_a| = 3$?