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Extensions 1→N→G→Q→1 with N=C2×C6 and Q=C2×C12

Direct product G=N×Q with N=C2×C6 and Q=C2×C12
dρLabelID
C22×C6×C12288C2^2xC6xC12288,1018

Semidirect products G=N:Q with N=C2×C6 and Q=C2×C12
extensionφ:Q→Aut NdρLabelID
(C2×C6)⋊1(C2×C12) = C4×S3×A4φ: C2×C12/C4 → C6 ⊆ Aut C2×C6366(C2xC6):1(C2xC12)288,919
(C2×C6)⋊2(C2×C12) = C2×Dic3×A4φ: C2×C12/C22 → C6 ⊆ Aut C2×C672(C2xC6):2(C2xC12)288,927
(C2×C6)⋊3(C2×C12) = C3×S3×C22⋊C4φ: C2×C12/C6 → C22 ⊆ Aut C2×C648(C2xC6):3(C2xC12)288,651
(C2×C6)⋊4(C2×C12) = C3×Dic3⋊4D4φ: C2×C12/C6 → C22 ⊆ Aut C2×C648(C2xC6):4(C2xC12)288,652
(C2×C6)⋊5(C2×C12) = C3×D4×Dic3φ: C2×C12/C6 → C22 ⊆ Aut C2×C648(C2xC6):5(C2xC12)288,705
(C2×C6)⋊6(C2×C12) = A4×C2×C12φ: C2×C12/C2×C4 → C3 ⊆ Aut C2×C672(C2xC6):6(C2xC12)288,979
(C2×C6)⋊7(C2×C12) = D4×C3×C12φ: C2×C12/C12 → C2 ⊆ Aut C2×C6144(C2xC6):7(C2xC12)288,815
(C2×C6)⋊8(C2×C12) = C12×C3⋊D4φ: C2×C12/C12 → C2 ⊆ Aut C2×C648(C2xC6):8(C2xC12)288,699
(C2×C6)⋊9(C2×C12) = S3×C22×C12φ: C2×C12/C12 → C2 ⊆ Aut C2×C696(C2xC6):9(C2xC12)288,989
(C2×C6)⋊10(C2×C12) = C22⋊C4×C3×C6φ: C2×C12/C2×C6 → C2 ⊆ Aut C2×C6144(C2xC6):10(C2xC12)288,812
(C2×C6)⋊11(C2×C12) = C6×C6.D4φ: C2×C12/C2×C6 → C2 ⊆ Aut C2×C648(C2xC6):11(C2xC12)288,723
(C2×C6)⋊12(C2×C12) = Dic3×C22×C6φ: C2×C12/C2×C6 → C2 ⊆ Aut C2×C696(C2xC6):12(C2xC12)288,1001

Non-split extensions G=N.Q with N=C2×C6 and Q=C2×C12
extensionφ:Q→Aut NdρLabelID
(C2×C6).1(C2×C12) = C3×C23.6D6φ: C2×C12/C6 → C22 ⊆ Aut C2×C6244(C2xC6).1(C2xC12)288,240
(C2×C6).2(C2×C12) = C3×C12.46D4φ: C2×C12/C6 → C22 ⊆ Aut C2×C6484(C2xC6).2(C2xC12)288,257
(C2×C6).3(C2×C12) = C3×C12.47D4φ: C2×C12/C6 → C22 ⊆ Aut C2×C6484(C2xC6).3(C2xC12)288,258
(C2×C6).4(C2×C12) = C3×C23.16D6φ: C2×C12/C6 → C22 ⊆ Aut C2×C648(C2xC6).4(C2xC12)288,648
(C2×C6).5(C2×C12) = C3×S3×M4(2)φ: C2×C12/C6 → C22 ⊆ Aut C2×C6484(C2xC6).5(C2xC12)288,677
(C2×C6).6(C2×C12) = C3×D12.C4φ: C2×C12/C6 → C22 ⊆ Aut C2×C6484(C2xC6).6(C2xC12)288,678
(C2×C6).7(C2×C12) = C3×D4.Dic3φ: C2×C12/C6 → C22 ⊆ Aut C2×C6484(C2xC6).7(C2xC12)288,719
(C2×C6).8(C2×C12) = C2×C4×C3.A4φ: C2×C12/C2×C4 → C3 ⊆ Aut C2×C672(C2xC6).8(C2xC12)288,343
(C2×C6).9(C2×C12) = D4×C36φ: C2×C12/C12 → C2 ⊆ Aut C2×C6144(C2xC6).9(C2xC12)288,168
(C2×C6).10(C2×C12) = C9×C8○D4φ: C2×C12/C12 → C2 ⊆ Aut C2×C61442(C2xC6).10(C2xC12)288,181
(C2×C6).11(C2×C12) = C32×C8○D4φ: C2×C12/C12 → C2 ⊆ Aut C2×C6144(C2xC6).11(C2xC12)288,828
(C2×C6).12(C2×C12) = Dic3×C24φ: C2×C12/C12 → C2 ⊆ Aut C2×C696(C2xC6).12(C2xC12)288,247
(C2×C6).13(C2×C12) = C3×Dic3⋊C8φ: C2×C12/C12 → C2 ⊆ Aut C2×C696(C2xC6).13(C2xC12)288,248
(C2×C6).14(C2×C12) = C3×C24⋊C4φ: C2×C12/C12 → C2 ⊆ Aut C2×C696(C2xC6).14(C2xC12)288,249
(C2×C6).15(C2×C12) = C3×D6⋊C8φ: C2×C12/C12 → C2 ⊆ Aut C2×C696(C2xC6).15(C2xC12)288,254
(C2×C6).16(C2×C12) = C3×C6.C42φ: C2×C12/C12 → C2 ⊆ Aut C2×C696(C2xC6).16(C2xC12)288,265
(C2×C6).17(C2×C12) = S3×C2×C24φ: C2×C12/C12 → C2 ⊆ Aut C2×C696(C2xC6).17(C2xC12)288,670
(C2×C6).18(C2×C12) = C6×C8⋊S3φ: C2×C12/C12 → C2 ⊆ Aut C2×C696(C2xC6).18(C2xC12)288,671
(C2×C6).19(C2×C12) = C3×C8○D12φ: C2×C12/C12 → C2 ⊆ Aut C2×C6482(C2xC6).19(C2xC12)288,672
(C2×C6).20(C2×C12) = Dic3×C2×C12φ: C2×C12/C12 → C2 ⊆ Aut C2×C696(C2xC6).20(C2xC12)288,693
(C2×C6).21(C2×C12) = C6×Dic3⋊C4φ: C2×C12/C12 → C2 ⊆ Aut C2×C696(C2xC6).21(C2xC12)288,694
(C2×C6).22(C2×C12) = C6×D6⋊C4φ: C2×C12/C12 → C2 ⊆ Aut C2×C696(C2xC6).22(C2xC12)288,698
(C2×C6).23(C2×C12) = C9×C23⋊C4φ: C2×C12/C2×C6 → C2 ⊆ Aut C2×C6724(C2xC6).23(C2xC12)288,49
(C2×C6).24(C2×C12) = C9×C4.D4φ: C2×C12/C2×C6 → C2 ⊆ Aut C2×C6724(C2xC6).24(C2xC12)288,50
(C2×C6).25(C2×C12) = C9×C4.10D4φ: C2×C12/C2×C6 → C2 ⊆ Aut C2×C61444(C2xC6).25(C2xC12)288,51
(C2×C6).26(C2×C12) = C22⋊C4×C18φ: C2×C12/C2×C6 → C2 ⊆ Aut C2×C6144(C2xC6).26(C2xC12)288,165
(C2×C6).27(C2×C12) = C9×C42⋊C2φ: C2×C12/C2×C6 → C2 ⊆ Aut C2×C6144(C2xC6).27(C2xC12)288,167
(C2×C6).28(C2×C12) = M4(2)×C18φ: C2×C12/C2×C6 → C2 ⊆ Aut C2×C6144(C2xC6).28(C2xC12)288,180
(C2×C6).29(C2×C12) = C32×C23⋊C4φ: C2×C12/C2×C6 → C2 ⊆ Aut C2×C672(C2xC6).29(C2xC12)288,317
(C2×C6).30(C2×C12) = C32×C4.D4φ: C2×C12/C2×C6 → C2 ⊆ Aut C2×C672(C2xC6).30(C2xC12)288,318
(C2×C6).31(C2×C12) = C32×C4.10D4φ: C2×C12/C2×C6 → C2 ⊆ Aut C2×C6144(C2xC6).31(C2xC12)288,319
(C2×C6).32(C2×C12) = C32×C42⋊C2φ: C2×C12/C2×C6 → C2 ⊆ Aut C2×C6144(C2xC6).32(C2xC12)288,814
(C2×C6).33(C2×C12) = M4(2)×C3×C6φ: C2×C12/C2×C6 → C2 ⊆ Aut C2×C6144(C2xC6).33(C2xC12)288,827
(C2×C6).34(C2×C12) = C12×C3⋊C8φ: C2×C12/C2×C6 → C2 ⊆ Aut C2×C696(C2xC6).34(C2xC12)288,236
(C2×C6).35(C2×C12) = C3×C42.S3φ: C2×C12/C2×C6 → C2 ⊆ Aut C2×C696(C2xC6).35(C2xC12)288,237
(C2×C6).36(C2×C12) = C3×C12⋊C8φ: C2×C12/C2×C6 → C2 ⊆ Aut C2×C696(C2xC6).36(C2xC12)288,238
(C2×C6).37(C2×C12) = C3×C12.55D4φ: C2×C12/C2×C6 → C2 ⊆ Aut C2×C648(C2xC6).37(C2xC12)288,264
(C2×C6).38(C2×C12) = C3×C12.D4φ: C2×C12/C2×C6 → C2 ⊆ Aut C2×C6244(C2xC6).38(C2xC12)288,267
(C2×C6).39(C2×C12) = C3×C23.7D6φ: C2×C12/C2×C6 → C2 ⊆ Aut C2×C6244(C2xC6).39(C2xC12)288,268
(C2×C6).40(C2×C12) = C3×C12.10D4φ: C2×C12/C2×C6 → C2 ⊆ Aut C2×C6484(C2xC6).40(C2xC12)288,270
(C2×C6).41(C2×C12) = C2×C6×C3⋊C8φ: C2×C12/C2×C6 → C2 ⊆ Aut C2×C696(C2xC6).41(C2xC12)288,691
(C2×C6).42(C2×C12) = C6×C4.Dic3φ: C2×C12/C2×C6 → C2 ⊆ Aut C2×C648(C2xC6).42(C2xC12)288,692
(C2×C6).43(C2×C12) = C6×C4⋊Dic3φ: C2×C12/C2×C6 → C2 ⊆ Aut C2×C696(C2xC6).43(C2xC12)288,696
(C2×C6).44(C2×C12) = C3×C23.26D6φ: C2×C12/C2×C6 → C2 ⊆ Aut C2×C648(C2xC6).44(C2xC12)288,697
(C2×C6).45(C2×C12) = C9×C2.C42central extension (φ=1)288(C2xC6).45(C2xC12)288,45
(C2×C6).46(C2×C12) = C9×C8⋊C4central extension (φ=1)288(C2xC6).46(C2xC12)288,47
(C2×C6).47(C2×C12) = C9×C22⋊C8central extension (φ=1)144(C2xC6).47(C2xC12)288,48
(C2×C6).48(C2×C12) = C9×C4⋊C8central extension (φ=1)288(C2xC6).48(C2xC12)288,55
(C2×C6).49(C2×C12) = C4⋊C4×C18central extension (φ=1)288(C2xC6).49(C2xC12)288,166
(C2×C6).50(C2×C12) = C32×C2.C42central extension (φ=1)288(C2xC6).50(C2xC12)288,313
(C2×C6).51(C2×C12) = C32×C8⋊C4central extension (φ=1)288(C2xC6).51(C2xC12)288,315
(C2×C6).52(C2×C12) = C32×C22⋊C8central extension (φ=1)144(C2xC6).52(C2xC12)288,316
(C2×C6).53(C2×C12) = C32×C4⋊C8central extension (φ=1)288(C2xC6).53(C2xC12)288,323
(C2×C6).54(C2×C12) = C4⋊C4×C3×C6central extension (φ=1)288(C2xC6).54(C2xC12)288,813

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