On groups whose conjugacy class sizes are not divisible by each other

Let G be a finite group and N (G) be the set of its conjugacy class sizes excluding~1. Let us define a directed graph (G), the set of vertices of this graph is N (G) and the vertices x and y are connected by a directed edge from x to y if x divides y and N (G) does not contain a number z different from x and y such that x divides z and z divides y. We will call the graph (G) the conjugate graph of the group G. In this work, we will study finite groups whose conjugate graph is a set of points.