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Abel-Grassmann’s groupoid and neutrosophic extended triplet loop are two important algebraic structures that describe two kinds of generalized symmetries. In this paper, we investigate quasi AG-neutrosophic extended triplet loop, which is a fusion structure of the two kinds of algebraic structures mentioned above. We propose new notions of AG-(l,r)-Loop and AG-(r,l)-Loop, deeply study their basic properties and structural characteristics, and prove strictly the following statements: (1) each strong AG-(l,r)-Loop can be represented as the union of its disjoint sub-AG-groups, (2) the concepts of strong AG-(l,r)-Loop, strong AG-(l,l)-Loop, and AG-(l,lr)-Loop are equivalent, and (3) the concepts of strong AG-(r,l)-Loop and strong AG-(r,r)-Loop are equivalent.