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

Direct product G=N×Q with N=C3×C6 and Q=C4⋊C4
dρLabelID
C4⋊C4×C3×C6288C4:C4xC3xC6288,813

Semidirect products G=N:Q with N=C3×C6 and Q=C4⋊C4
extensionφ:Q→Aut NdρLabelID
(C3×C6)⋊1(C4⋊C4) = C2×C3⋊S3.Q8φ: C4⋊C4/C2 → D4 ⊆ Aut C3×C648(C3xC6):1(C4:C4)288,882
(C3×C6)⋊2(C4⋊C4) = C2×C2.PSU3(𝔽2)φ: C4⋊C4/C2 → Q8 ⊆ Aut C3×C648(C3xC6):2(C4:C4)288,894
(C3×C6)⋊3(C4⋊C4) = C2×C4⋊(C32⋊C4)φ: C4⋊C4/C4 → C4 ⊆ Aut C3×C648(C3xC6):3(C4:C4)288,933
(C3×C6)⋊4(C4⋊C4) = C2×Dic3⋊Dic3φ: C4⋊C4/C22 → C22 ⊆ Aut C3×C696(C3xC6):4(C4:C4)288,613
(C3×C6)⋊5(C4⋊C4) = C2×C62.C22φ: C4⋊C4/C22 → C22 ⊆ Aut C3×C696(C3xC6):5(C4:C4)288,615
(C3×C6)⋊6(C4⋊C4) = C6×Dic3⋊C4φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C3×C696(C3xC6):6(C4:C4)288,694
(C3×C6)⋊7(C4⋊C4) = C6×C4⋊Dic3φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C3×C696(C3xC6):7(C4:C4)288,696
(C3×C6)⋊8(C4⋊C4) = C2×C6.Dic6φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C3×C6288(C3xC6):8(C4:C4)288,780
(C3×C6)⋊9(C4⋊C4) = C2×C12⋊Dic3φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C3×C6288(C3xC6):9(C4:C4)288,782

Non-split extensions G=N.Q with N=C3×C6 and Q=C4⋊C4
extensionφ:Q→Aut NdρLabelID
(C3×C6).1(C4⋊C4) = C32⋊C4⋊C8φ: C4⋊C4/C2 → D4 ⊆ Aut C3×C6484(C3xC6).1(C4:C4)288,380
(C3×C6).2(C4⋊C4) = C4.19S3≀C2φ: C4⋊C4/C2 → D4 ⊆ Aut C3×C6484(C3xC6).2(C4:C4)288,381
(C3×C6).3(C4⋊C4) = C62.D4φ: C4⋊C4/C2 → D4 ⊆ Aut C3×C648(C3xC6).3(C4:C4)288,385
(C3×C6).4(C4⋊C4) = C62.6D4φ: C4⋊C4/C2 → D4 ⊆ Aut C3×C696(C3xC6).4(C4:C4)288,390
(C3×C6).5(C4⋊C4) = C62.7D4φ: C4⋊C4/C2 → D4 ⊆ Aut C3×C696(C3xC6).5(C4:C4)288,391
(C3×C6).6(C4⋊C4) = C4.4PSU3(𝔽2)φ: C4⋊C4/C2 → Q8 ⊆ Aut C3×C6488(C3xC6).6(C4:C4)288,392
(C3×C6).7(C4⋊C4) = C4.PSU3(𝔽2)φ: C4⋊C4/C2 → Q8 ⊆ Aut C3×C6488(C3xC6).7(C4:C4)288,393
(C3×C6).8(C4⋊C4) = C4.2PSU3(𝔽2)φ: C4⋊C4/C2 → Q8 ⊆ Aut C3×C6488(C3xC6).8(C4:C4)288,394
(C3×C6).9(C4⋊C4) = C62.Q8φ: C4⋊C4/C2 → Q8 ⊆ Aut C3×C648(C3xC6).9(C4:C4)288,395
(C3×C6).10(C4⋊C4) = C62.2Q8φ: C4⋊C4/C2 → Q8 ⊆ Aut C3×C6488-(C3xC6).10(C4:C4)288,396
(C3×C6).11(C4⋊C4) = C8⋊(C32⋊C4)φ: C4⋊C4/C4 → C4 ⊆ Aut C3×C6484(C3xC6).11(C4:C4)288,416
(C3×C6).12(C4⋊C4) = C3⋊S3.4D8φ: C4⋊C4/C4 → C4 ⊆ Aut C3×C6484(C3xC6).12(C4:C4)288,417
(C3×C6).13(C4⋊C4) = (C3×C24).C4φ: C4⋊C4/C4 → C4 ⊆ Aut C3×C6484(C3xC6).13(C4:C4)288,418
(C3×C6).14(C4⋊C4) = C8.(C32⋊C4)φ: C4⋊C4/C4 → C4 ⊆ Aut C3×C6484(C3xC6).14(C4:C4)288,419
(C3×C6).15(C4⋊C4) = (C3×C12)⋊4C8φ: C4⋊C4/C4 → C4 ⊆ Aut C3×C696(C3xC6).15(C4:C4)288,424
(C3×C6).16(C4⋊C4) = C32⋊5(C4⋊C8)φ: C4⋊C4/C4 → C4 ⊆ Aut C3×C696(C3xC6).16(C4:C4)288,427
(C3×C6).17(C4⋊C4) = (C6×C12)⋊2C4φ: C4⋊C4/C4 → C4 ⊆ Aut C3×C648(C3xC6).17(C4:C4)288,429
(C3×C6).18(C4⋊C4) = C12.81D12φ: C4⋊C4/C22 → C22 ⊆ Aut C3×C696(C3xC6).18(C4:C4)288,219
(C3×C6).19(C4⋊C4) = C12.15Dic6φ: C4⋊C4/C22 → C22 ⊆ Aut C3×C696(C3xC6).19(C4:C4)288,220
(C3×C6).20(C4⋊C4) = C12.Dic6φ: C4⋊C4/C22 → C22 ⊆ Aut C3×C696(C3xC6).20(C4:C4)288,221
(C3×C6).21(C4⋊C4) = C12.6Dic6φ: C4⋊C4/C22 → C22 ⊆ Aut C3×C696(C3xC6).21(C4:C4)288,222
(C3×C6).22(C4⋊C4) = C6.18D24φ: C4⋊C4/C22 → C22 ⊆ Aut C3×C696(C3xC6).22(C4:C4)288,223
(C3×C6).23(C4⋊C4) = C12.8Dic6φ: C4⋊C4/C22 → C22 ⊆ Aut C3×C696(C3xC6).23(C4:C4)288,224
(C3×C6).24(C4⋊C4) = C12.82D12φ: C4⋊C4/C22 → C22 ⊆ Aut C3×C6484(C3xC6).24(C4:C4)288,225
(C3×C6).25(C4⋊C4) = C62.5Q8φ: C4⋊C4/C22 → C22 ⊆ Aut C3×C6484(C3xC6).25(C4:C4)288,226
(C3×C6).26(C4⋊C4) = C62.6Q8φ: C4⋊C4/C22 → C22 ⊆ Aut C3×C696(C3xC6).26(C4:C4)288,227
(C3×C6).27(C4⋊C4) = C3×C12⋊C8φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C3×C696(C3xC6).27(C4:C4)288,238
(C3×C6).28(C4⋊C4) = C3×C6.Q16φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C3×C696(C3xC6).28(C4:C4)288,241
(C3×C6).29(C4⋊C4) = C3×C12.Q8φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C3×C696(C3xC6).29(C4:C4)288,242
(C3×C6).30(C4⋊C4) = C3×Dic3⋊C8φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C3×C696(C3xC6).30(C4:C4)288,248
(C3×C6).31(C4⋊C4) = C3×C8⋊Dic3φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C3×C696(C3xC6).31(C4:C4)288,251
(C3×C6).32(C4⋊C4) = C3×C24⋊1C4φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C3×C696(C3xC6).32(C4:C4)288,252
(C3×C6).33(C4⋊C4) = C3×C24.C4φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C3×C6482(C3xC6).33(C4:C4)288,253
(C3×C6).34(C4⋊C4) = C3×C12.53D4φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C3×C6484(C3xC6).34(C4:C4)288,256
(C3×C6).35(C4⋊C4) = C3×C6.C42φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C3×C696(C3xC6).35(C4:C4)288,265
(C3×C6).36(C4⋊C4) = C12.57D12φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C3×C6288(C3xC6).36(C4:C4)288,279
(C3×C6).37(C4⋊C4) = C12.9Dic6φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C3×C6288(C3xC6).37(C4:C4)288,282
(C3×C6).38(C4⋊C4) = C12.10Dic6φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C3×C6288(C3xC6).38(C4:C4)288,283
(C3×C6).39(C4⋊C4) = C12.30Dic6φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C3×C6288(C3xC6).39(C4:C4)288,289
(C3×C6).40(C4⋊C4) = C24⋊2Dic3φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C3×C6288(C3xC6).40(C4:C4)288,292
(C3×C6).41(C4⋊C4) = C24⋊1Dic3φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C3×C6288(C3xC6).41(C4:C4)288,293
(C3×C6).42(C4⋊C4) = C12.59D12φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C3×C6144(C3xC6).42(C4:C4)288,294
(C3×C6).43(C4⋊C4) = C62.8Q8φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C3×C6144(C3xC6).43(C4:C4)288,297
(C3×C6).44(C4⋊C4) = C62.15Q8φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C3×C6288(C3xC6).44(C4:C4)288,306
(C3×C6).45(C4⋊C4) = C32×C2.C42central extension (φ=1)288(C3xC6).45(C4:C4)288,313
(C3×C6).46(C4⋊C4) = C32×C4⋊C8central extension (φ=1)288(C3xC6).46(C4:C4)288,323
(C3×C6).47(C4⋊C4) = C32×C4.Q8central extension (φ=1)288(C3xC6).47(C4:C4)288,324
(C3×C6).48(C4⋊C4) = C32×C2.D8central extension (φ=1)288(C3xC6).48(C4:C4)288,325
(C3×C6).49(C4⋊C4) = C32×C8.C4central extension (φ=1)144(C3xC6).49(C4:C4)288,326

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