# Extensions 1→N→G→Q→1 with N=C3×C6 and Q=C2×C4

Direct product G=N×Q with N=C3×C6 and Q=C2×C4
dρLabelID
C2×C6×C12144C2xC6xC12144,178

Semidirect products G=N:Q with N=C3×C6 and Q=C2×C4
extensionφ:Q→Aut NdρLabelID
(C3×C6)⋊1(C2×C4) = C22×C32⋊C4φ: C2×C4/C2C4 ⊆ Aut C3×C624(C3xC6):1(C2xC4)144,191
(C3×C6)⋊2(C2×C4) = C2×S3×Dic3φ: C2×C4/C2C22 ⊆ Aut C3×C648(C3xC6):2(C2xC4)144,146
(C3×C6)⋊3(C2×C4) = C2×C6.D6φ: C2×C4/C2C22 ⊆ Aut C3×C624(C3xC6):3(C2xC4)144,149
(C3×C6)⋊4(C2×C4) = S3×C2×C12φ: C2×C4/C4C2 ⊆ Aut C3×C648(C3xC6):4(C2xC4)144,159
(C3×C6)⋊5(C2×C4) = C2×C4×C3⋊S3φ: C2×C4/C4C2 ⊆ Aut C3×C672(C3xC6):5(C2xC4)144,169
(C3×C6)⋊6(C2×C4) = Dic3×C2×C6φ: C2×C4/C22C2 ⊆ Aut C3×C648(C3xC6):6(C2xC4)144,166
(C3×C6)⋊7(C2×C4) = C22×C3⋊Dic3φ: C2×C4/C22C2 ⊆ Aut C3×C6144(C3xC6):7(C2xC4)144,176

Non-split extensions G=N.Q with N=C3×C6 and Q=C2×C4
extensionφ:Q→Aut NdρLabelID
(C3×C6).1(C2×C4) = C3⋊S33C8φ: C2×C4/C2C4 ⊆ Aut C3×C6244(C3xC6).1(C2xC4)144,130
(C3×C6).2(C2×C4) = C32⋊M4(2)φ: C2×C4/C2C4 ⊆ Aut C3×C6244(C3xC6).2(C2xC4)144,131
(C3×C6).3(C2×C4) = C4×C32⋊C4φ: C2×C4/C2C4 ⊆ Aut C3×C6244(C3xC6).3(C2xC4)144,132
(C3×C6).4(C2×C4) = C4⋊(C32⋊C4)φ: C2×C4/C2C4 ⊆ Aut C3×C6244(C3xC6).4(C2xC4)144,133
(C3×C6).5(C2×C4) = C2×C322C8φ: C2×C4/C2C4 ⊆ Aut C3×C648(C3xC6).5(C2xC4)144,134
(C3×C6).6(C2×C4) = C62.C4φ: C2×C4/C2C4 ⊆ Aut C3×C6244-(C3xC6).6(C2xC4)144,135
(C3×C6).7(C2×C4) = C62⋊C4φ: C2×C4/C2C4 ⊆ Aut C3×C6124+(C3xC6).7(C2xC4)144,136
(C3×C6).8(C2×C4) = S3×C3⋊C8φ: C2×C4/C2C22 ⊆ Aut C3×C6484(C3xC6).8(C2xC4)144,52
(C3×C6).9(C2×C4) = C12.29D6φ: C2×C4/C2C22 ⊆ Aut C3×C6244(C3xC6).9(C2xC4)144,53
(C3×C6).10(C2×C4) = D6.Dic3φ: C2×C4/C2C22 ⊆ Aut C3×C6484(C3xC6).10(C2xC4)144,54
(C3×C6).11(C2×C4) = C12.31D6φ: C2×C4/C2C22 ⊆ Aut C3×C6244(C3xC6).11(C2xC4)144,55
(C3×C6).12(C2×C4) = Dic32φ: C2×C4/C2C22 ⊆ Aut C3×C648(C3xC6).12(C2xC4)144,63
(C3×C6).13(C2×C4) = D6⋊Dic3φ: C2×C4/C2C22 ⊆ Aut C3×C648(C3xC6).13(C2xC4)144,64
(C3×C6).14(C2×C4) = C6.D12φ: C2×C4/C2C22 ⊆ Aut C3×C624(C3xC6).14(C2xC4)144,65
(C3×C6).15(C2×C4) = Dic3⋊Dic3φ: C2×C4/C2C22 ⊆ Aut C3×C648(C3xC6).15(C2xC4)144,66
(C3×C6).16(C2×C4) = C62.C22φ: C2×C4/C2C22 ⊆ Aut C3×C648(C3xC6).16(C2xC4)144,67
(C3×C6).17(C2×C4) = S3×C24φ: C2×C4/C4C2 ⊆ Aut C3×C6482(C3xC6).17(C2xC4)144,69
(C3×C6).18(C2×C4) = C3×C8⋊S3φ: C2×C4/C4C2 ⊆ Aut C3×C6482(C3xC6).18(C2xC4)144,70
(C3×C6).19(C2×C4) = Dic3×C12φ: C2×C4/C4C2 ⊆ Aut C3×C648(C3xC6).19(C2xC4)144,76
(C3×C6).20(C2×C4) = C3×Dic3⋊C4φ: C2×C4/C4C2 ⊆ Aut C3×C648(C3xC6).20(C2xC4)144,77
(C3×C6).21(C2×C4) = C3×D6⋊C4φ: C2×C4/C4C2 ⊆ Aut C3×C648(C3xC6).21(C2xC4)144,79
(C3×C6).22(C2×C4) = C8×C3⋊S3φ: C2×C4/C4C2 ⊆ Aut C3×C672(C3xC6).22(C2xC4)144,85
(C3×C6).23(C2×C4) = C24⋊S3φ: C2×C4/C4C2 ⊆ Aut C3×C672(C3xC6).23(C2xC4)144,86
(C3×C6).24(C2×C4) = C4×C3⋊Dic3φ: C2×C4/C4C2 ⊆ Aut C3×C6144(C3xC6).24(C2xC4)144,92
(C3×C6).25(C2×C4) = C6.Dic6φ: C2×C4/C4C2 ⊆ Aut C3×C6144(C3xC6).25(C2xC4)144,93
(C3×C6).26(C2×C4) = C6.11D12φ: C2×C4/C4C2 ⊆ Aut C3×C672(C3xC6).26(C2xC4)144,95
(C3×C6).27(C2×C4) = C6×C3⋊C8φ: C2×C4/C22C2 ⊆ Aut C3×C648(C3xC6).27(C2xC4)144,74
(C3×C6).28(C2×C4) = C3×C4.Dic3φ: C2×C4/C22C2 ⊆ Aut C3×C6242(C3xC6).28(C2xC4)144,75
(C3×C6).29(C2×C4) = C3×C4⋊Dic3φ: C2×C4/C22C2 ⊆ Aut C3×C648(C3xC6).29(C2xC4)144,78
(C3×C6).30(C2×C4) = C3×C6.D4φ: C2×C4/C22C2 ⊆ Aut C3×C624(C3xC6).30(C2xC4)144,84
(C3×C6).31(C2×C4) = C2×C324C8φ: C2×C4/C22C2 ⊆ Aut C3×C6144(C3xC6).31(C2xC4)144,90
(C3×C6).32(C2×C4) = C12.58D6φ: C2×C4/C22C2 ⊆ Aut C3×C672(C3xC6).32(C2xC4)144,91
(C3×C6).33(C2×C4) = C12⋊Dic3φ: C2×C4/C22C2 ⊆ Aut C3×C6144(C3xC6).33(C2xC4)144,94
(C3×C6).34(C2×C4) = C625C4φ: C2×C4/C22C2 ⊆ Aut C3×C672(C3xC6).34(C2xC4)144,100
(C3×C6).35(C2×C4) = C32×C22⋊C4central extension (φ=1)72(C3xC6).35(C2xC4)144,102
(C3×C6).36(C2×C4) = C32×C4⋊C4central extension (φ=1)144(C3xC6).36(C2xC4)144,103
(C3×C6).37(C2×C4) = C32×M4(2)central extension (φ=1)72(C3xC6).37(C2xC4)144,105

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