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Extensions 1→N→G→Q→1 with N=D6 and Q=C2×C3⋊S3

Direct product G=N×Q with N=D6 and Q=C2×C3⋊S3
dρLabelID
C22×S3×C3⋊S372C2^2xS3xC3:S3432,768

Semidirect products G=N:Q with N=D6 and Q=C2×C3⋊S3
extensionφ:Q→Out NdρLabelID
D6⋊1(C2×C3⋊S3) = C3⋊S3×D12φ: C2×C3⋊S3/C3⋊S3 → C2 ⊆ Out D672D6:1(C2xC3:S3)432,672
D6⋊2(C2×C3⋊S3) = C12⋊S32φ: C2×C3⋊S3/C3⋊S3 → C2 ⊆ Out D672D6:2(C2xC3:S3)432,673
D6⋊3(C2×C3⋊S3) = C3⋊S3×C3⋊D4φ: C2×C3⋊S3/C3⋊S3 → C2 ⊆ Out D672D6:3(C2xC3:S3)432,685
D6⋊4(C2×C3⋊S3) = C62⋊23D6φ: C2×C3⋊S3/C3⋊S3 → C2 ⊆ Out D636D6:4(C2xC3:S3)432,686
D6⋊5(C2×C3⋊S3) = C2×C33⋊6D4φ: C2×C3⋊S3/C3×C6 → C2 ⊆ Out D6144D6:5(C2xC3:S3)432,680
D6⋊6(C2×C3⋊S3) = C2×C33⋊7D4φ: C2×C3⋊S3/C3×C6 → C2 ⊆ Out D672D6:6(C2xC3:S3)432,681
D6⋊7(C2×C3⋊S3) = S3×C32⋊7D4φ: C2×C3⋊S3/C3×C6 → C2 ⊆ Out D672D6:7(C2xC3:S3)432,684

Non-split extensions G=N.Q with N=D6 and Q=C2×C3⋊S3
extensionφ:Q→Out NdρLabelID
D6.1(C2×C3⋊S3) = (C3×D12)⋊S3φ: C2×C3⋊S3/C3⋊S3 → C2 ⊆ Out D6144D6.1(C2xC3:S3)432,661
D6.2(C2×C3⋊S3) = D12⋊(C3⋊S3)φ: C2×C3⋊S3/C3⋊S3 → C2 ⊆ Out D672D6.2(C2xC3:S3)432,662
D6.3(C2×C3⋊S3) = C62.90D6φ: C2×C3⋊S3/C3⋊S3 → C2 ⊆ Out D672D6.3(C2xC3:S3)432,675
D6.4(C2×C3⋊S3) = C62.91D6φ: C2×C3⋊S3/C3⋊S3 → C2 ⊆ Out D672D6.4(C2xC3:S3)432,676
D6.5(C2×C3⋊S3) = C12.73S32φ: C2×C3⋊S3/C3×C6 → C2 ⊆ Out D672D6.5(C2xC3:S3)432,667
D6.6(C2×C3⋊S3) = C12.57S32φ: C2×C3⋊S3/C3×C6 → C2 ⊆ Out D6144D6.6(C2xC3:S3)432,668
D6.7(C2×C3⋊S3) = C12.58S32φ: C2×C3⋊S3/C3×C6 → C2 ⊆ Out D672D6.7(C2xC3:S3)432,669
D6.8(C2×C3⋊S3) = S3×C32⋊4Q8φ: trivial image144D6.8(C2xC3:S3)432,660
D6.9(C2×C3⋊S3) = C4×S3×C3⋊S3φ: trivial image72D6.9(C2xC3:S3)432,670
D6.10(C2×C3⋊S3) = S3×C12⋊S3φ: trivial image72D6.10(C2xC3:S3)432,671
D6.11(C2×C3⋊S3) = C2×S3×C3⋊Dic3φ: trivial image144D6.11(C2xC3:S3)432,674

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