Eighty three stationary points of MgC6H2 isomers spanning from 0 to 215 kcal mol(-1) have been theoretically identified using density functional theory at the B3LYP/6-311d-+G(2d,2p) level of theory. Among them, four low-lying isomers lying within 23.06 kcal mol(-1) (1 eV) have been further characterized in detail using high-level coupled-cluster (CC) methods. The thermodynamically most stable isomer turns out to be 1-magnesacyclohepta-4-en-2,6-diyne (1). The other three isomers, 3-magnesahepta-1,4,6-triyne (2), 1-magnesacyclohepta-2,3,4-trien-6-yne (3), and 1-magnesahepta-2,4,6-triyne (4) lie 8.24, 19.76, and 21.36 kcal mol(-1), respectively, above 1 at the ae-CCSD(T)/cc-pCVTZ level of theory. All the four isomers are polar with a permanent electric dipole moment (mu not equal 0). Hence, they are potential candidates for rotational spectroscopic studies. Considering the recent identification of magnesium-bearing hydrocarbons such as, MgC2H and MgC4H in IRC+10216, it is believed that the current theoretical data may be of relevance to laboratory molecular spectroscopic and radioastronomical studies on MgC6H2 isomers. The energetic and spectroscopic information gathered in this study would aid the detection of low-lying MgC6H2 isomers in the laboratory, which are indispensable for radioastronomical studies. It is also noted here that neither the National Institute of Standards and Technology Chemistry WebBook nor the Kinetic Database for Astrochemistry lists any isomer of MgC6H2 at the moment. Therefore, these isomers are studied here theoretically for the very first time.