Isoorderly permutable subgroups of finite groups

Let $A$ and $B$ be subgroups of a finite group $G$. Then the subgroup $A$ is called: isoorderly permutable with $B$ if there is a subgroup $C$ of $G$ such that $|C| = |B|$ and $AC = CA$, hereditarily isoorderly permutable with $B$ if $A$ is isoorderly permutable with $B$ in any subgroup of $G$ containing $A$ and $B$, isoorderly permutable in $G$ if $A$ is isoorderly permutable with every subgroup of $G$, and hereditarily isoorderly permutable in $G$ if $A$ is hereditarily isoorderly permutable with every subgroup of $G$. In this paper, the properties of isoorderly permutable subgroups are analyzed, and the structure of a finite group $G$ all of whose minimal subgroups are hereditarily isoorderly permutable is studied.