  Let B be an extriangulated category with enough projectives and enough
injectives. Let
  C be a fully rigid subcategory of B which admits a twin cotorsion pair
((C,K),(K,D)). The quotient category B/K is abelian, we assume that it is
hereditary and has finite length. In this article, we study the relation
between support tilting subcategories of B/K and maximal relative rigid
subcategories of B. More precisely, we show that the image of any cluster
tilting subcategory of B is support tilting in B/K and any support tilting
subcategory in B/K can be lifted to a unique relative maximal rigid subcategory
in B. We also give a bijection between these two classes of subcategories if C
is generated by an object.
