Unique factorization does not hold up to order statistics-equivalence

Statement
There is no unique factorization result for finite groups up to order statistics-equivalence. In particular, it is possible for a fact about::directly indecomposable group to be order statistics-equivalent to a group that is isomorphic to the fact about::external direct product of strictly smaller groups.

Related facts

 * Krull-Remak-Schmidt theorem states that a unique factorization result does hold up to the strict notion of isomorphism.
 * Order statistics-equivalence is finite-direct product-closed
 * 1-isomorphism is direct product-closed
 * Direct product is cancellative for order statistics-equivalence