Finite groups with the most Chermak-Delgado measures of subgroups

Let $G$ be a finite group and $H\le G$. The Chermak-Delgado measure of $H$ is defined as the number $\mathrm{\mid }H\mathrm{\mid }\cdot \mathrm{\mid }{C}_G(H)\mathrm{\mid }$. In this paper, we identify finite groups that exhibit the maximum number of Chermak-Delgado measures under some specific conditions.