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Extensions 1→N→G→Q→1 with N=C3×C6 and Q=Dic6

Direct product G=N×Q with N=C3×C6 and Q=Dic6
dρLabelID
C3×C6×Dic6144C3xC6xDic6432,700

Semidirect products G=N:Q with N=C3×C6 and Q=Dic6
extensionφ:Q→Aut NdρLabelID
(C3×C6)⋊Dic6 = C2×He3⋊2Q8φ: Dic6/C2 → D6 ⊆ Aut C3×C6144(C3xC6):Dic6432,316
(C3×C6)⋊2Dic6 = C2×C33⋊Q8φ: Dic6/C3 → Q8 ⊆ Aut C3×C6488(C3xC6):2Dic6432,758
(C3×C6)⋊3Dic6 = C2×He3⋊3Q8φ: Dic6/C4 → S3 ⊆ Aut C3×C6144(C3xC6):3Dic6432,348
(C3×C6)⋊4Dic6 = C2×He3⋊4Q8φ: Dic6/C4 → S3 ⊆ Aut C3×C6144(C3xC6):4Dic6432,384
(C3×C6)⋊5Dic6 = C2×C33⋊4Q8φ: Dic6/C6 → C22 ⊆ Aut C3×C6144(C3xC6):5Dic6432,683
(C3×C6)⋊6Dic6 = C2×C33⋊5Q8φ: Dic6/C6 → C22 ⊆ Aut C3×C648(C3xC6):6Dic6432,695
(C3×C6)⋊7Dic6 = C6×C32⋊2Q8φ: Dic6/Dic3 → C2 ⊆ Aut C3×C648(C3xC6):7Dic6432,657
(C3×C6)⋊8Dic6 = C6×C32⋊4Q8φ: Dic6/C12 → C2 ⊆ Aut C3×C6144(C3xC6):8Dic6432,710
(C3×C6)⋊9Dic6 = C2×C33⋊8Q8φ: Dic6/C12 → C2 ⊆ Aut C3×C6432(C3xC6):9Dic6432,720

Non-split extensions G=N.Q with N=C3×C6 and Q=Dic6
extensionφ:Q→Aut NdρLabelID
(C3×C6).1Dic6 = C62.D6φ: Dic6/C2 → D6 ⊆ Aut C3×C6144(C3xC6).1Dic6432,95
(C3×C6).2Dic6 = C62.3D6φ: Dic6/C2 → D6 ⊆ Aut C3×C6144(C3xC6).2Dic6432,96
(C3×C6).3Dic6 = C6.PSU3(𝔽2)φ: Dic6/C3 → Q8 ⊆ Aut C3×C6488(C3xC6).3Dic6432,592
(C3×C6).4Dic6 = C6.2PSU3(𝔽2)φ: Dic6/C3 → Q8 ⊆ Aut C3×C6488(C3xC6).4Dic6432,593
(C3×C6).5Dic6 = C62.19D6φ: Dic6/C4 → S3 ⊆ Aut C3×C6144(C3xC6).5Dic6432,139
(C3×C6).6Dic6 = C62.20D6φ: Dic6/C4 → S3 ⊆ Aut C3×C6144(C3xC6).6Dic6432,140
(C3×C6).7Dic6 = Dic9⋊C12φ: Dic6/C4 → S3 ⊆ Aut C3×C6144(C3xC6).7Dic6432,145
(C3×C6).8Dic6 = C36⋊C12φ: Dic6/C4 → S3 ⊆ Aut C3×C6144(C3xC6).8Dic6432,146
(C3×C6).9Dic6 = C62.29D6φ: Dic6/C4 → S3 ⊆ Aut C3×C6144(C3xC6).9Dic6432,187
(C3×C6).10Dic6 = C62.30D6φ: Dic6/C4 → S3 ⊆ Aut C3×C6144(C3xC6).10Dic6432,188
(C3×C6).11Dic6 = C2×C36.C6φ: Dic6/C4 → S3 ⊆ Aut C3×C6144(C3xC6).11Dic6432,352
(C3×C6).12Dic6 = Dic9⋊Dic3φ: Dic6/C6 → C22 ⊆ Aut C3×C6144(C3xC6).12Dic6432,88
(C3×C6).13Dic6 = C18.Dic6φ: Dic6/C6 → C22 ⊆ Aut C3×C6144(C3xC6).13Dic6432,89
(C3×C6).14Dic6 = Dic3⋊Dic9φ: Dic6/C6 → C22 ⊆ Aut C3×C6144(C3xC6).14Dic6432,90
(C3×C6).15Dic6 = C2×C9⋊Dic6φ: Dic6/C6 → C22 ⊆ Aut C3×C6144(C3xC6).15Dic6432,303
(C3×C6).16Dic6 = C62.80D6φ: Dic6/C6 → C22 ⊆ Aut C3×C6144(C3xC6).16Dic6432,452
(C3×C6).17Dic6 = C62.82D6φ: Dic6/C6 → C22 ⊆ Aut C3×C6144(C3xC6).17Dic6432,454
(C3×C6).18Dic6 = C62.85D6φ: Dic6/C6 → C22 ⊆ Aut C3×C648(C3xC6).18Dic6432,462
(C3×C6).19Dic6 = C3×Dic3⋊Dic3φ: Dic6/Dic3 → C2 ⊆ Aut C3×C648(C3xC6).19Dic6432,428
(C3×C6).20Dic6 = C3×C62.C22φ: Dic6/Dic3 → C2 ⊆ Aut C3×C648(C3xC6).20Dic6432,429
(C3×C6).21Dic6 = C62.81D6φ: Dic6/Dic3 → C2 ⊆ Aut C3×C6144(C3xC6).21Dic6432,453
(C3×C6).22Dic6 = C3×Dic9⋊C4φ: Dic6/C12 → C2 ⊆ Aut C3×C6144(C3xC6).22Dic6432,129
(C3×C6).23Dic6 = C3×C4⋊Dic9φ: Dic6/C12 → C2 ⊆ Aut C3×C6144(C3xC6).23Dic6432,130
(C3×C6).24Dic6 = C6.Dic18φ: Dic6/C12 → C2 ⊆ Aut C3×C6432(C3xC6).24Dic6432,181
(C3×C6).25Dic6 = C36⋊Dic3φ: Dic6/C12 → C2 ⊆ Aut C3×C6432(C3xC6).25Dic6432,182
(C3×C6).26Dic6 = C6×Dic18φ: Dic6/C12 → C2 ⊆ Aut C3×C6144(C3xC6).26Dic6432,340
(C3×C6).27Dic6 = C2×C12.D9φ: Dic6/C12 → C2 ⊆ Aut C3×C6432(C3xC6).27Dic6432,380
(C3×C6).28Dic6 = C3×C6.Dic6φ: Dic6/C12 → C2 ⊆ Aut C3×C6144(C3xC6).28Dic6432,488
(C3×C6).29Dic6 = C3×C12⋊Dic3φ: Dic6/C12 → C2 ⊆ Aut C3×C6144(C3xC6).29Dic6432,489
(C3×C6).30Dic6 = C62.146D6φ: Dic6/C12 → C2 ⊆ Aut C3×C6432(C3xC6).30Dic6432,504
(C3×C6).31Dic6 = C62.147D6φ: Dic6/C12 → C2 ⊆ Aut C3×C6432(C3xC6).31Dic6432,505
(C3×C6).32Dic6 = C32×Dic3⋊C4central extension (φ=1)144(C3xC6).32Dic6432,472
(C3×C6).33Dic6 = C32×C4⋊Dic3central extension (φ=1)144(C3xC6).33Dic6432,473

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