The issue of characterizing classes of argumentation frameworks where different semantics agree has been considered in the literature with main focus on the relationships between agreement and topological properties. This paper contributes to this kind of investigation from a complementary perspective, by introducing a systematic classification of agreement classes concerning a comprehensive set of argumentation semantics on the basis of properties of their sets of extensions only. In particular, it is shown that 14 distinct classes out of 120 nominal ones exist, and a complete analysis of their set-theoretical relationships is carried out.