Farrokhi–Safa lower-bound conjecture for the number of commutativity degrees

Let $G$ be a finite group. For a group $X$, let $l_M(X)$ denote the maximum length of chains of subgroups of $X$, and let $\mathcal{D}(G)$ be the set of commutativity degrees of $G$.

Farrokhi–Safa's weaker conjecture. Every finite group $G$ satisfies

$$|\mathcal{D}(G)|\geqslant l_M\left(\frac{G}{Z(G)}\right)+1.$$

This is stated as a weaker version of the preceding conjecture, giving a lower bound for the number of distinct commutativity degrees in terms of the subgroup-chain length of the central quotient. It is presented without a resolution in the source.