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Extensions 1→N→G→Q→1 with N=C56.C4 and Q=C2

Direct product G=N×Q with N=C56.C4 and Q=C2
dρLabelID
C2×C56.C4224C2xC56.C4448,641

Semidirect products G=N:Q with N=C56.C4 and Q=C2
extensionφ:Q→Out NdρLabelID
C56.C4⋊1C2 = D56.1C4φ: C2/C1 → C2 ⊆ Out C56.C42242C56.C4:1C2448,67
C56.C4⋊2C2 = D8.Dic7φ: C2/C1 → C2 ⊆ Out C56.C41124C56.C4:2C2448,120
C56.C4⋊3C2 = C56.23D4φ: C2/C1 → C2 ⊆ Out C56.C41124C56.C4:3C2448,694
C56.C4⋊4C2 = C56.29D4φ: C2/C1 → C2 ⊆ Out C56.C42244C56.C4:4C2448,726
C56.C4⋊5C2 = C28.58D8φ: C2/C1 → C2 ⊆ Out C56.C42244C56.C4:5C2448,124
C56.C4⋊6C2 = D7×C8.C4φ: C2/C1 → C2 ⊆ Out C56.C41124C56.C4:6C2448,426
C56.C4⋊7C2 = M4(2).25D14φ: C2/C1 → C2 ⊆ Out C56.C41124C56.C4:7C2448,427
C56.C4⋊8C2 = D8⋊5Dic7φ: C2/C1 → C2 ⊆ Out C56.C41124C56.C4:8C2448,730
C56.C4⋊9C2 = D8⋊4Dic7φ: C2/C1 → C2 ⊆ Out C56.C41124C56.C4:9C2448,731
C56.C4⋊10C2 = C56.44D4φ: C2/C1 → C2 ⊆ Out C56.C41124C56.C4:10C2448,711
C56.C4⋊11C2 = C28.3D8φ: C2/C1 → C2 ⊆ Out C56.C41124+C56.C4:11C2448,73
C56.C4⋊12C2 = D56⋊4C4φ: C2/C1 → C2 ⊆ Out C56.C41124C56.C4:12C2448,251
C56.C4⋊13C2 = M4(2).Dic7φ: C2/C1 → C2 ⊆ Out C56.C41124C56.C4:13C2448,659
C56.C4⋊14C2 = D4.3D28φ: C2/C1 → C2 ⊆ Out C56.C41124C56.C4:14C2448,675
C56.C4⋊15C2 = D4.4D28φ: C2/C1 → C2 ⊆ Out C56.C41124+C56.C4:15C2448,676
C56.C4⋊16C2 = D4.5D28φ: C2/C1 → C2 ⊆ Out C56.C42244-C56.C4:16C2448,677
C56.C4⋊17C2 = D56⋊11C4φ: trivial image1122C56.C4:17C2448,234

Non-split extensions G=N.Q with N=C56.C4 and Q=C2
extensionφ:Q→Out NdρLabelID
C56.C4.1C2 = C112.C4φ: C2/C1 → C2 ⊆ Out C56.C42242C56.C4.1C2448,63
C56.C4.2C2 = Q16.Dic7φ: C2/C1 → C2 ⊆ Out C56.C42244C56.C4.2C2448,122
C56.C4.3C2 = C8.7Dic14φ: C2/C1 → C2 ⊆ Out C56.C42244C56.C4.3C2448,50
C56.C4.4C2 = C56.Q8φ: C2/C1 → C2 ⊆ Out C56.C41124C56.C4.4C2448,44
C56.C4.5C2 = C16⋊Dic7φ: C2/C1 → C2 ⊆ Out C56.C41124C56.C4.5C2448,70
C56.C4.6C2 = C28.4D8φ: C2/C1 → C2 ⊆ Out C56.C42244-C56.C4.6C2448,74

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