Cosets and Lagrange's Theorem · Challenge problem

$GL(2,\mathbb Z_3)$, the invertible $2\times2$ matrices over $\mathbb Z_3$, has order $48$. Let $H$ be the subgroup of upper-triangular invertible matrices $\begin{pmatrix}a&b\\0&d\end{pmatrix}$ with $a,d\ne0$. What is $[GL(2,\mathbb Z_3):H]$?