two mat-tabs in one component

Question

Im looking for a way to include encompass two mat-tabs of an angular mat-tab group in one component for including in a parent component which has the mat-tab-group in its template, ie.

parent.html

<mat-tab-group>
  <mat-tab> First tab </mat-tab>
  <child-component-with-two-tabs></child-component-with-two-tabs>
</mat-tab-group>

I need to do this because the two tabs of the child component have some common logic and I don't want to use a service. Just having the two mat-tabs in the child component template does not work (why is that?). My instinct tells me I need to have something like a component with two templates, but I could not find anything on this.