Recall that a subgroup $H$ of a group $G$ is called a TI-subgroup if for every $g \in G$ it is $H \cap H^g \in \{1,H\}$. We say that a group $G$ is a DTI-group if the derived subgroups of all of its subgroups are TI-subgroups.

Question: Is the class of DTI-groups closed under taking quotients?