  Let $G$ be a finite group, $L_1(G)$ be its poset of cyclic subgroups and
consider the quantity $\alpha(G)=\frac{|L_1(G)|}{|G|}$. The aim of this paper
is to study the class $\cal{C}$ of finite nilpotent groups having
$\alpha(G)=\frac{3}{4}$. We show that if $G$ belongs to this class, then it is
a 2-group satisfying certain conditions. Also, we study the appartenance of
some classes of finite groups to $\cal{C}$.
