Cosets and Lagrange's Theorem · Challenge problem

$D_{24}$ is the group of symmetries of a regular $24$-gon, order $48$, generated by a rotation $r$ of order $24$ and a reflection $s$. The element $r^{12}$ has order $2$ and is central (commutes with everything). Let $H=\langle s, r^{12}\rangle$. What is $[D_{24}:H]$?