Cosets and Lagrange's Theorem · Challenge problem

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