Let N be a normal subgroup of a finite group G. In the recent past years some results have appeared concerning the influence of the G-class sizes of N, that is, with the sizes of the conjugacy classes in G contained in N, on the structure of N. In this survey, we present the main results and techniques used for proving that any normal subgroup of G which has exactly three G-conjugacy class sizes is solvable. Thus, we obtain a generalisation for normal subgroups of the classical N. It?'s theorem which asserts that those finite groups having three class sizes axe solvable, and in particular, a new proof of it is provided.
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