Finite groups with three relative commutativity degrees

For a finite group GG and a subgroup HH of GG, the relative commutativity degree of HH in GG, denoted by d(H,G)d(H,G), is the probability that an element of HH commutes with an element of GG. Let mathcalD(G)=d(H,G):HleqGmathcalD(G)=d(H,G):HleqG be the set of all relative commutativity degrees of subgroups of GG. It is shown that a finite group GG admits three relative commutativity degrees if and only if G/Z(G)G/Z(G) is a non-cyclic group of order pqpq, where pp and qq are primes. Moreover, we determine all the relative commutativity degrees of some known groups.