Trees · Challenge problem

The $2 \times 4$ ladder graph has $2$ rows of $4$ vertices each: vertices $1,2,3,4$ form the top row, vertices $5,6,7,8$ form the bottom row. Horizontal edges connect $1\text{-}2, 2\text{-}3, 3\text{-}4$ (top) and $5\text{-}6, 6\text{-}7, 7\text{-}8$ (bottom); vertical edges connect $1\text{-}5, 2\text{-}6, 3\text{-}7, 4\text{-}8$ (rungs). How many spanning trees does this graph have?