A finite invariant set of a continuous map of an interval induces apermutation called its type. If this permutation is a cycle, it is calledits orbit type. It has been shown by Geller and Tolosa thatMisiurewicz–Nitecki orbit types of period $n$ congruent to $1$ (mod 4)andtheirgeneralizations to orbit types of period $n$ congruent to $3$(mod 4) havemaximal entropy among all orbit types of odd period $n$, and indeedamongall permutations of period $n$. We further generalize this family topermutations of even period $n$ and show that they again attain maximalentropyamongst $n$-permutations.