The so--called subgroup commutativity degree sd(G) of a finite group G is
the number of permuting subgroups (H,K)∈L(G)×L(G), where L(G) is the subgroup lattice of G, divided
by ∣L(G)∣2. It allows us to measure how G is far from the
celebrated classification of quasihamiltonian groups of K. Iwasawa. Here we
generalize sd(G), looking at suitable sublattices of L(G), and
show some new lower bounds.Comment: 8 pages; to appear in Bull. Belgian Math. Soc. with revision