Period of the over-under shuffle on 14 cards

A deck is held face down and dealt one card at a time into the other hand: the second card goes on top of the first, the third goes underneath, the fourth on top, and so on alternately until all are moved. Repeating this shuffle eventually restores the original order; for $4$ cards it takes $3$ shuffles, and for $2,4,8,16,32,64$ cards it takes $2,3,4,5,6,7$ shuffles. How many shuffles restore a $14$-card deck?

$14$. Writing one shuffle as a permutation of the $14$ positions and following where card $1$ goes, the permutation turns out to be a single $14$-cycle. The order of a permutation is the lcm of its cycle lengths, so exactly $14$ shuffles are needed (a direct simulation agrees).