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The cis- and trans-isomers of 6-(3-(3,4-dichlorophenyl)-1,2,4-oxadiazol-5-yl)cyclohex-3-ene-1-carboxylic acid (cis-A and trans-A) were obtained by the reaction of 3,4-dichloro-N′-hydroxybenzimidamide and cis-1,2,3,6-tetrahydrophthalic anhydride. Cocrystals of cis-A with appropriate solvents (cis-A‧½(1,2-DCE), cis-A‧½(1,2-DBE), and cis-A‧½C6H14) were grown from 1,2-dichloroethane (1,2-DCE), 1,2-dibromoethane (1,2-DBE), and a n-hexane/CHCl3 mixture and then characterized by X-ray crystallography. In their structures, cis-A is self-assembled to give a hybrid 2D supramolecular organic framework (SOF) formed by the cooperative action of O–H⋯O hydrogen bonding, Cl⋯O halogen bonding, and π⋯π stacking. The self-assembled cis-A divides the space between the 2D SOF layers into infinite hollow tunnels incorporating solvent molecules. The energy contribution of each noncovalent interaction to the occurrence of the 2D SOF was verified by several theoretical approaches, including MEP and combined QTAIM and NCIplot analyses. The consideration of the theoretical data proved that hydrogen bonding (approx. −15.2 kcal/mol) is the most important interaction, followed by π⋯π stacking (approx. −11.1 kcal/mol); meanwhile, the contribution of halogen bonding (approx. −3.6 kcal/mol) is the smallest among these interactions. The structure of the isomeric compound trans-A does not exhibit a 2D SOF architecture. It is assembled by the combined action of hydrogen bonding and π⋯π stacking, without the involvement of halogen bonds. A comparison of the cis-A structures with that of trans-A indicated that halogen bonding, although it has the lowest energy in cis-A-based cocrystals, plays a significant role in the crystal design of the hybrid 2D SOF. The majority of the reported porous halogen-bonded organic frameworks were assembled via iodine and bromine-based contacts, while chlorine-based systems—which, in our case, are structure-directing—were unknown before this study.