FINITE GROUPS WITH LARGE CHERMAK–DELGADO LATTICES

Abstract Given a finite group G , we denote by $L(G)$ the subgroup lattice of G and by ${\cal CD}(G)$ the Chermak–Delgado lattice of G . In this note, we determine the finite groups G such that $|{\cal CD}(G)|=|L(G)|-k$ , for $k=1,2$ .