Trees · Challenge problem

The Mobius-Kantor-style graph $M$ has the $6$-cycle $1\text{-}2\text{-}3\text{-}4\text{-}5\text{-}6\text{-}1$ together with the three "long" diagonals $14, 25, 36$ joining opposite vertices. Use the Matrix-Tree Theorem to find the number of spanning trees of $M$.