# Extensions 1→N→G→Q→1 with N=C3×C6 and Q=C2×A4

Direct product G=N×Q with N=C3×C6 and Q=C2×A4
dρLabelID
A4×C62108A4xC6^2432,770

Semidirect products G=N:Q with N=C3×C6 and Q=C2×A4
extensionφ:Q→Aut NdρLabelID
(C3×C6)⋊(C2×A4) = C2×C62⋊C6φ: C2×A4/C22C6 ⊆ Aut C3×C6186+(C3xC6):(C2xA4)432,542
(C3×C6)⋊2(C2×A4) = C22×C32⋊A4φ: C2×A4/C23C3 ⊆ Aut C3×C636(C3xC6):2(C2xA4)432,550
(C3×C6)⋊3(C2×A4) = S3×C6×A4φ: C2×A4/A4C2 ⊆ Aut C3×C6366(C3xC6):3(C2xA4)432,763
(C3×C6)⋊4(C2×A4) = C2×A4×C3⋊S3φ: C2×A4/A4C2 ⊆ Aut C3×C654(C3xC6):4(C2xA4)432,764

Non-split extensions G=N.Q with N=C3×C6 and Q=C2×A4
extensionφ:Q→Aut NdρLabelID
(C3×C6).1(C2×A4) = C6.(S3×A4)φ: C2×A4/C22C6 ⊆ Aut C3×C67212+(C3xC6).1(C2xA4)432,269
(C3×C6).2(C2×A4) = Q8⋊He3⋊C2φ: C2×A4/C22C6 ⊆ Aut C3×C67212-(C3xC6).2(C2xA4)432,270
(C3×C6).3(C2×A4) = C624C12φ: C2×A4/C22C6 ⊆ Aut C3×C6366-(C3xC6).3(C2xA4)432,272
(C3×C6).4(C2×A4) = C4×C32.A4φ: C2×A4/C23C3 ⊆ Aut C3×C6363(C3xC6).4(C2xA4)432,332
(C3×C6).5(C2×A4) = C4×C32⋊A4φ: C2×A4/C23C3 ⊆ Aut C3×C6363(C3xC6).5(C2xA4)432,333
(C3×C6).6(C2×A4) = C2×Q8⋊3- 1+2φ: C2×A4/C23C3 ⊆ Aut C3×C6144(C3xC6).6(C2xA4)432,335
(C3×C6).7(C2×A4) = C2×Q8⋊He3φ: C2×A4/C23C3 ⊆ Aut C3×C6144(C3xC6).7(C2xA4)432,336
(C3×C6).8(C2×A4) = Q8⋊C94C6φ: C2×A4/C23C3 ⊆ Aut C3×C6726(C3xC6).8(C2xA4)432,338
(C3×C6).9(C2×A4) = C4○D4⋊He3φ: C2×A4/C23C3 ⊆ Aut C3×C6726(C3xC6).9(C2xA4)432,339
(C3×C6).10(C2×A4) = C22×C32.A4φ: C2×A4/C23C3 ⊆ Aut C3×C636(C3xC6).10(C2xA4)432,549
(C3×C6).11(C2×A4) = Q8⋊C93S3φ: C2×A4/A4C2 ⊆ Aut C3×C61444(C3xC6).11(C2xA4)432,267
(C3×C6).12(C2×A4) = S3×Q8⋊C9φ: C2×A4/A4C2 ⊆ Aut C3×C61444(C3xC6).12(C2xA4)432,268
(C3×C6).13(C2×A4) = Dic3×C3.A4φ: C2×A4/A4C2 ⊆ Aut C3×C6366(C3xC6).13(C2xA4)432,271
(C3×C6).14(C2×A4) = C2×S3×C3.A4φ: C2×A4/A4C2 ⊆ Aut C3×C6366(C3xC6).14(C2xA4)432,541
(C3×C6).15(C2×A4) = C3×Dic3.A4φ: C2×A4/A4C2 ⊆ Aut C3×C6484(C3xC6).15(C2xA4)432,622
(C3×C6).16(C2×A4) = C3×S3×SL2(𝔽3)φ: C2×A4/A4C2 ⊆ Aut C3×C6484(C3xC6).16(C2xA4)432,623
(C3×C6).17(C2×A4) = C3×Dic3×A4φ: C2×A4/A4C2 ⊆ Aut C3×C6366(C3xC6).17(C2xA4)432,624
(C3×C6).18(C2×A4) = C3⋊Dic3.2A4φ: C2×A4/A4C2 ⊆ Aut C3×C6144(C3xC6).18(C2xA4)432,625
(C3×C6).19(C2×A4) = C3⋊S3×SL2(𝔽3)φ: C2×A4/A4C2 ⊆ Aut C3×C672(C3xC6).19(C2xA4)432,626
(C3×C6).20(C2×A4) = A4×C3⋊Dic3φ: C2×A4/A4C2 ⊆ Aut C3×C6108(C3xC6).20(C2xA4)432,627
(C3×C6).21(C2×A4) = C12×C3.A4central extension (φ=1)108(C3xC6).21(C2xA4)432,331
(C3×C6).22(C2×A4) = C6×Q8⋊C9central extension (φ=1)432(C3xC6).22(C2xA4)432,334
(C3×C6).23(C2×A4) = C3×Q8.C18central extension (φ=1)216(C3xC6).23(C2xA4)432,337
(C3×C6).24(C2×A4) = C2×C6×C3.A4central extension (φ=1)108(C3xC6).24(C2xA4)432,548
(C3×C6).25(C2×A4) = A4×C3×C12central extension (φ=1)108(C3xC6).25(C2xA4)432,697
(C3×C6).26(C2×A4) = C3×C6×SL2(𝔽3)central extension (φ=1)144(C3xC6).26(C2xA4)432,698
(C3×C6).27(C2×A4) = C32×C4.A4central extension (φ=1)144(C3xC6).27(C2xA4)432,699

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