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Group-theoretical methods are used to enumerate the structures of ordered double perovskites, A2BB'X6, in which the ordering of cations B and B' into alternate octahedra is considered in combination with the ubiquitous BX6 (or B'X6) octahedral tilting. The cation ordering on the B-cation site is described by the irreducible representation R_1^+ of the Pm \overline 3 m space group of the cubic aristotype, while the octahedral tilting is mediated by irreducible representations M_3^+ and R_4^+. There are 12 different structures identified, and the corresponding group-subgroup relationships are displayed. Known structures are briefly reviewed.

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