Finite groups with dense $\mathcal{C}\mathcal{D}$-subgroups

A group $G$ is said to have dense $\mathcal{C}\mathcal{D}$-subgroups if each non-empty open interval of the subgroup lattice $L(G)$ contains a subgroup in the Chermak–Delgado lattice $\mathcal{C}\mathcal{D}(G)$. In this note, we study finite groups satisfying this property.