I think that quotient groups are relatively important topic and we certainly have some questions about them. We do have tags for normal-subgroups and for quotient-spaces. As far as the importance of the topic and frequency of questions asked here on MSE are concerned, I'd say that these concepts are comparable.
Should we introduce the tag quotient-groups?
Quotient groups and normal subgroups are very closely related topics. So maybe other reasonable way to go would be to have them in the same tag. (In this case I think the base way to proceed would be to create the tag quotient-groups and make the two tags synonymous. Creating the tag synonym would mean that if someone starts typing quotient in the tags field, the tag (quotient-groups) is offered to them as one of the possibilities.) Of course, if we have both topics in the same tag, it should be mentioned also in the tag-info. At the moment the tag-excerpt and the tag-wiki for (normal-subgroups) are rather short. But since the content of the tag seems to be clear from the name of the tag, I do not think that this is a problem.
Would it be better to have these two topics in the same tag? (So that we do not create too many tags.)