# Extensions 1→N→G→Q→1 with N=C2×C3⋊S3 and Q=C2×C6

Direct product G=N×Q with N=C2×C3⋊S3 and Q=C2×C6
dρLabelID
C3⋊S3×C22×C6144C3:S3xC2^2xC6432,773

Semidirect products G=N:Q with N=C2×C3⋊S3 and Q=C2×C6
extensionφ:Q→Out NdρLabelID
(C2×C3⋊S3)⋊1(C2×C6) = C2×He34D4φ: C2×C6/C2C6 ⊆ Out C2×C3⋊S372(C2xC3:S3):1(C2xC6)432,350
(C2×C3⋊S3)⋊2(C2×C6) = D4×C32⋊C6φ: C2×C6/C2C6 ⊆ Out C2×C3⋊S33612+(C2xC3:S3):2(C2xC6)432,360
(C2×C3⋊S3)⋊3(C2×C6) = C2×He36D4φ: C2×C6/C2C6 ⊆ Out C2×C3⋊S372(C2xC3:S3):3(C2xC6)432,377
(C2×C3⋊S3)⋊4(C2×C6) = C3×S3×D12φ: C2×C6/C3C22 ⊆ Out C2×C3⋊S3484(C2xC3:S3):4(C2xC6)432,649
(C2×C3⋊S3)⋊5(C2×C6) = C3×S3×C3⋊D4φ: C2×C6/C3C22 ⊆ Out C2×C3⋊S3244(C2xC3:S3):5(C2xC6)432,658
(C2×C3⋊S3)⋊6(C2×C6) = C23×C32⋊C6φ: C2×C6/C22C3 ⊆ Out C2×C3⋊S372(C2xC3:S3):6(C2xC6)432,558
(C2×C3⋊S3)⋊7(C2×C6) = C6×C3⋊D12φ: C2×C6/C6C2 ⊆ Out C2×C3⋊S348(C2xC3:S3):7(C2xC6)432,656
(C2×C3⋊S3)⋊8(C2×C6) = C3×Dic3⋊D6φ: C2×C6/C6C2 ⊆ Out C2×C3⋊S3244(C2xC3:S3):8(C2xC6)432,659
(C2×C3⋊S3)⋊9(C2×C6) = C6×C12⋊S3φ: C2×C6/C6C2 ⊆ Out C2×C3⋊S3144(C2xC3:S3):9(C2xC6)432,712
(C2×C3⋊S3)⋊10(C2×C6) = C3×D4×C3⋊S3φ: C2×C6/C6C2 ⊆ Out C2×C3⋊S372(C2xC3:S3):10(C2xC6)432,714
(C2×C3⋊S3)⋊11(C2×C6) = C6×C327D4φ: C2×C6/C6C2 ⊆ Out C2×C3⋊S372(C2xC3:S3):11(C2xC6)432,719
(C2×C3⋊S3)⋊12(C2×C6) = S32×C2×C6φ: C2×C6/C6C2 ⊆ Out C2×C3⋊S348(C2xC3:S3):12(C2xC6)432,767

Non-split extensions G=N.Q with N=C2×C3⋊S3 and Q=C2×C6
extensionφ:Q→Out NdρLabelID
(C2×C3⋊S3).1(C2×C6) = C62.36D6φ: C2×C6/C2C6 ⊆ Out C2×C3⋊S3726(C2xC3:S3).1(C2xC6)432,351
(C2×C3⋊S3).2(C2×C6) = C62.13D6φ: C2×C6/C2C6 ⊆ Out C2×C3⋊S37212-(C2xC3:S3).2(C2xC6)432,361
(C2×C3⋊S3).3(C2×C6) = (Q8×He3)⋊C2φ: C2×C6/C2C6 ⊆ Out C2×C3⋊S37212+(C2xC3:S3).3(C2xC6)432,369
(C2×C3⋊S3).4(C2×C6) = C3×S32⋊C4φ: C2×C6/C3C22 ⊆ Out C2×C3⋊S3244(C2xC3:S3).4(C2xC6)432,574
(C2×C3⋊S3).5(C2×C6) = C3×C3⋊S3.Q8φ: C2×C6/C3C22 ⊆ Out C2×C3⋊S3484(C2xC3:S3).5(C2xC6)432,575
(C2×C3⋊S3).6(C2×C6) = C3×C2.PSU3(𝔽2)φ: C2×C6/C3C22 ⊆ Out C2×C3⋊S3488(C2xC3:S3).6(C2xC6)432,591
(C2×C3⋊S3).7(C2×C6) = C3×D6.6D6φ: C2×C6/C3C22 ⊆ Out C2×C3⋊S3484(C2xC3:S3).7(C2xC6)432,647
(C2×C3⋊S3).8(C2×C6) = C3×D6.3D6φ: C2×C6/C3C22 ⊆ Out C2×C3⋊S3244(C2xC3:S3).8(C2xC6)432,652
(C2×C3⋊S3).9(C2×C6) = C6×S3≀C2φ: C2×C6/C3C22 ⊆ Out C2×C3⋊S3244(C2xC3:S3).9(C2xC6)432,754
(C2×C3⋊S3).10(C2×C6) = C6×PSU3(𝔽2)φ: C2×C6/C3C22 ⊆ Out C2×C3⋊S3488(C2xC3:S3).10(C2xC6)432,757
(C2×C3⋊S3).11(C2×C6) = C2×C4×C32⋊C6φ: C2×C6/C22C3 ⊆ Out C2×C3⋊S372(C2xC3:S3).11(C2xC6)432,349
(C2×C3⋊S3).12(C2×C6) = Q8×C32⋊C6φ: C2×C6/C22C3 ⊆ Out C2×C3⋊S37212-(C2xC3:S3).12(C2xC6)432,368
(C2×C3⋊S3).13(C2×C6) = C12×C32⋊C4φ: C2×C6/C6C2 ⊆ Out C2×C3⋊S3484(C2xC3:S3).13(C2xC6)432,630
(C2×C3⋊S3).14(C2×C6) = C3×C4⋊(C32⋊C4)φ: C2×C6/C6C2 ⊆ Out C2×C3⋊S3484(C2xC3:S3).14(C2xC6)432,631
(C2×C3⋊S3).15(C2×C6) = C3×C62⋊C4φ: C2×C6/C6C2 ⊆ Out C2×C3⋊S3244(C2xC3:S3).15(C2xC6)432,634
(C2×C3⋊S3).16(C2×C6) = C3×D12⋊S3φ: C2×C6/C6C2 ⊆ Out C2×C3⋊S3484(C2xC3:S3).16(C2xC6)432,644
(C2×C3⋊S3).17(C2×C6) = C3×Dic3.D6φ: C2×C6/C6C2 ⊆ Out C2×C3⋊S3484(C2xC3:S3).17(C2xC6)432,645
(C2×C3⋊S3).18(C2×C6) = C3×D6.D6φ: C2×C6/C6C2 ⊆ Out C2×C3⋊S3484(C2xC3:S3).18(C2xC6)432,646
(C2×C3⋊S3).19(C2×C6) = S32×C12φ: C2×C6/C6C2 ⊆ Out C2×C3⋊S3484(C2xC3:S3).19(C2xC6)432,648
(C2×C3⋊S3).20(C2×C6) = C3×D6⋊D6φ: C2×C6/C6C2 ⊆ Out C2×C3⋊S3484(C2xC3:S3).20(C2xC6)432,650
(C2×C3⋊S3).21(C2×C6) = C6×C6.D6φ: C2×C6/C6C2 ⊆ Out C2×C3⋊S348(C2xC3:S3).21(C2xC6)432,654
(C2×C3⋊S3).22(C2×C6) = C3×C12.59D6φ: C2×C6/C6C2 ⊆ Out C2×C3⋊S372(C2xC3:S3).22(C2xC6)432,713
(C2×C3⋊S3).23(C2×C6) = C3×C12.D6φ: C2×C6/C6C2 ⊆ Out C2×C3⋊S372(C2xC3:S3).23(C2xC6)432,715
(C2×C3⋊S3).24(C2×C6) = C3×C12.26D6φ: C2×C6/C6C2 ⊆ Out C2×C3⋊S3144(C2xC3:S3).24(C2xC6)432,717
(C2×C3⋊S3).25(C2×C6) = C2×C6×C32⋊C4φ: C2×C6/C6C2 ⊆ Out C2×C3⋊S348(C2xC3:S3).25(C2xC6)432,765
(C2×C3⋊S3).26(C2×C6) = C3⋊S3×C2×C12φ: trivial image144(C2xC3:S3).26(C2xC6)432,711
(C2×C3⋊S3).27(C2×C6) = C3×Q8×C3⋊S3φ: trivial image144(C2xC3:S3).27(C2xC6)432,716

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