  The noisy permutation channel is a useful abstraction introduced by Makur for
point-to-point communication networks and biological storage. While the
asymptotic capacity results exist for this model, the characterization of the
second-order asymptotics is not available. Therefore, we analyze the converse
bounds for the noisy permutation channel in the finite blocklength regime. To
do this, we present a modified minimax meta-converse for noisy permutation
channels by symbol relaxation. To derive the second-order asymptotics of the
converse bound, we propose a way to use divergence covering in analysis. It
enables the observation of the second-order asymptotics and the strong converse
via Berry-Esseen type bounds. These two conclusions hold for noisy permutation
channels with strictly positive matrices (entry-wise). In addition, we obtain
computable bounds for the noisy permutation channel with the binary symmetric
channel (BSC), including the original computable converse bound based on the
modified minimax meta-converse, the asymptotic expansion derived from our
subset covering technique, and the {\epsilon}-capacity result. We find that a
smaller crossover probability provides a higher upper bound for a fixed finite
blocklength, although the {\epsilon}-capacity is agnostic to the BSC parameter.
Finally, numerical results show that the normal approximation shows remarkable
precision, and our new converse bound is stronger than previous bounds.
