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Let B be an extriangulated category with enough projectives P and enough injectives I, and let R be a contravariantly finite rigid subcategory of B which contains P. We have an abelian quotient category H/R ⊆ B/R which is equivalent mod(R/P). In this article, we find a one-to-one correspondence between support τ -tilting (resp. τ -rigid) subcategories of H/R and maximal relative rigid (resp. relative rigid) subcategories of H, and show that support tilting subcategories in H/R is a special kind of support τ -tilting subcategories. We also study the relation between tilting subcategories of B/R and cluster tilting subcategories of B when R is cluster tilting.