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Extensions 1→N→G→Q→1 with N=D4 and Q=C3⋊D4

Direct product G=N×Q with N=D4 and Q=C3⋊D4
dρLabelID
D4×C3⋊D448D4xC3:D4192,1360

Semidirect products G=N:Q with N=D4 and Q=C3⋊D4
extensionφ:Q→Out NdρLabelID
D4⋊1(C3⋊D4) = Dic3⋊D8φ: C3⋊D4/Dic3 → C2 ⊆ Out D496D4:1(C3:D4)192,709
D4⋊2(C3⋊D4) = D12⋊D4φ: C3⋊D4/D6 → C2 ⊆ Out D448D4:2(C3:D4)192,715
D4⋊3(C3⋊D4) = Dic6⋊D4φ: C3⋊D4/D6 → C2 ⊆ Out D496D4:3(C3:D4)192,717
D4⋊4(C3⋊D4) = D12⋊18D4φ: C3⋊D4/D6 → C2 ⊆ Out D4248+D4:4(C3:D4)192,757
D4⋊5(C3⋊D4) = (C2×C6)⋊8D8φ: C3⋊D4/C2×C6 → C2 ⊆ Out D448D4:5(C3:D4)192,776
D4⋊6(C3⋊D4) = (C3×D4)⋊14D4φ: C3⋊D4/C2×C6 → C2 ⊆ Out D496D4:6(C3:D4)192,797
D4⋊7(C3⋊D4) = 2+ 1+4⋊6S3φ: C3⋊D4/C2×C6 → C2 ⊆ Out D4248+D4:7(C3:D4)192,800
D4⋊8(C3⋊D4) = C24.53D6φ: trivial image48D4:8(C3:D4)192,1365
D4⋊9(C3⋊D4) = C6.1042- 1+4φ: trivial image96D4:9(C3:D4)192,1383
D4⋊10(C3⋊D4) = C6.1452+ 1+4φ: trivial image48D4:10(C3:D4)192,1388

Non-split extensions G=N.Q with N=D4 and Q=C3⋊D4
extensionφ:Q→Out NdρLabelID
D4.1(C3⋊D4) = (C6×D8).C2φ: C3⋊D4/Dic3 → C2 ⊆ Out D496D4.1(C3:D4)192,712
D4.2(C3⋊D4) = Dic3⋊3SD16φ: C3⋊D4/Dic3 → C2 ⊆ Out D496D4.2(C3:D4)192,721
D4.3(C3⋊D4) = (C3×D4).D4φ: C3⋊D4/Dic3 → C2 ⊆ Out D496D4.3(C3:D4)192,724
D4.4(C3⋊D4) = M4(2).D6φ: C3⋊D4/Dic3 → C2 ⊆ Out D4488+D4.4(C3:D4)192,758
D4.5(C3⋊D4) = M4(2).13D6φ: C3⋊D4/Dic3 → C2 ⊆ Out D4488-D4.5(C3:D4)192,759
D4.6(C3⋊D4) = M4(2).15D6φ: C3⋊D4/Dic3 → C2 ⊆ Out D4488+D4.6(C3:D4)192,762
D4.7(C3⋊D4) = M4(2).16D6φ: C3⋊D4/Dic3 → C2 ⊆ Out D4968-D4.7(C3:D4)192,763
D4.8(C3⋊D4) = D6⋊6SD16φ: C3⋊D4/D6 → C2 ⊆ Out D448D4.8(C3:D4)192,728
D4.9(C3⋊D4) = Dic6.16D4φ: C3⋊D4/D6 → C2 ⊆ Out D496D4.9(C3:D4)192,732
D4.10(C3⋊D4) = D12.38D4φ: C3⋊D4/D6 → C2 ⊆ Out D4488-D4.10(C3:D4)192,760
D4.11(C3⋊D4) = D12.39D4φ: C3⋊D4/D6 → C2 ⊆ Out D4488+D4.11(C3:D4)192,761
D4.12(C3⋊D4) = D12.40D4φ: C3⋊D4/D6 → C2 ⊆ Out D4488-D4.12(C3:D4)192,764
D4.13(C3⋊D4) = (C3×D4).31D4φ: C3⋊D4/C2×C6 → C2 ⊆ Out D448D4.13(C3:D4)192,777
D4.14(C3⋊D4) = (C3×D4).32D4φ: C3⋊D4/C2×C6 → C2 ⊆ Out D496D4.14(C3:D4)192,798
D4.15(C3⋊D4) = 2+ 1+4.4S3φ: C3⋊D4/C2×C6 → C2 ⊆ Out D4488-D4.15(C3:D4)192,801
D4.16(C3⋊D4) = 2- 1+4⋊4S3φ: C3⋊D4/C2×C6 → C2 ⊆ Out D4488+D4.16(C3:D4)192,804
D4.17(C3⋊D4) = 2- 1+4.2S3φ: C3⋊D4/C2×C6 → C2 ⊆ Out D4488-D4.17(C3:D4)192,805
D4.18(C3⋊D4) = D12.32C23φ: trivial image488+D4.18(C3:D4)192,1394
D4.19(C3⋊D4) = D12.33C23φ: trivial image488-D4.19(C3:D4)192,1395
D4.20(C3⋊D4) = D12.34C23φ: trivial image488+D4.20(C3:D4)192,1396
D4.21(C3⋊D4) = D12.35C23φ: trivial image968-D4.21(C3:D4)192,1397

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