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Extensions 1→N→G→Q→1 with N=C22×C12 and Q=C6

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

Semidirect products G=N:Q with N=C22×C12 and Q=C6
extensionφ:Q→Aut NdρLabelID
(C22×C12)⋊1C6 = A4×D12φ: C6/C1 → C6 ⊆ Aut C22×C12366+(C2^2xC12):1C6288,920
(C22×C12)⋊2C6 = C4×S3×A4φ: C6/C1 → C6 ⊆ Aut C22×C12366(C2^2xC12):2C6288,919
(C22×C12)⋊3C6 = C3×D4×A4φ: C6/C1 → C6 ⊆ Aut C22×C12366(C2^2xC12):3C6288,980
(C22×C12)⋊4C6 = A4×C2×C12φ: C6/C2 → C3 ⊆ Aut C22×C1272(C2^2xC12):4C6288,979
(C22×C12)⋊5C6 = C6×D6⋊C4φ: C6/C3 → C2 ⊆ Aut C22×C1296(C2^2xC12):5C6288,698
(C22×C12)⋊6C6 = C3×C23.28D6φ: C6/C3 → C2 ⊆ Aut C22×C1248(C2^2xC12):6C6288,700
(C22×C12)⋊7C6 = C22⋊C4×C3×C6φ: C6/C3 → C2 ⊆ Aut C22×C12144(C2^2xC12):7C6288,812
(C22×C12)⋊8C6 = D4×C3×C12φ: C6/C3 → C2 ⊆ Aut C22×C12144(C2^2xC12):8C6288,815
(C22×C12)⋊9C6 = C32×C22.D4φ: C6/C3 → C2 ⊆ Aut C22×C12144(C2^2xC12):9C6288,820
(C22×C12)⋊10C6 = C3×C12⋊7D4φ: C6/C3 → C2 ⊆ Aut C22×C1248(C2^2xC12):10C6288,701
(C22×C12)⋊11C6 = C2×C6×D12φ: C6/C3 → C2 ⊆ Aut C22×C1296(C2^2xC12):11C6288,990
(C22×C12)⋊12C6 = C6×C4○D12φ: C6/C3 → C2 ⊆ Aut C22×C1248(C2^2xC12):12C6288,991
(C22×C12)⋊13C6 = C12×C3⋊D4φ: C6/C3 → C2 ⊆ Aut C22×C1248(C2^2xC12):13C6288,699
(C22×C12)⋊14C6 = S3×C22×C12φ: C6/C3 → C2 ⊆ Aut C22×C1296(C2^2xC12):14C6288,989
(C22×C12)⋊15C6 = C32×C4⋊D4φ: C6/C3 → C2 ⊆ Aut C22×C12144(C2^2xC12):15C6288,818
(C22×C12)⋊16C6 = D4×C62φ: C6/C3 → C2 ⊆ Aut C22×C12144(C2^2xC12):16C6288,1019
(C22×C12)⋊17C6 = C4○D4×C3×C6φ: C6/C3 → C2 ⊆ Aut C22×C12144(C2^2xC12):17C6288,1021

Non-split extensions G=N.Q with N=C22×C12 and Q=C6
extensionφ:Q→Aut NdρLabelID
(C22×C12).1C6 = A4×Dic6φ: C6/C1 → C6 ⊆ Aut C22×C12726-(C2^2xC12).1C6288,918
(C22×C12).2C6 = A4×C3⋊C8φ: C6/C1 → C6 ⊆ Aut C22×C12726(C2^2xC12).2C6288,408
(C22×C12).3C6 = D4×C3.A4φ: C6/C1 → C6 ⊆ Aut C22×C12366(C2^2xC12).3C6288,344
(C22×C12).4C6 = Q8×C3.A4φ: C6/C1 → C6 ⊆ Aut C22×C12726(C2^2xC12).4C6288,346
(C22×C12).5C6 = C3×Q8×A4φ: C6/C1 → C6 ⊆ Aut C22×C12726(C2^2xC12).5C6288,982
(C22×C12).6C6 = C8×C3.A4φ: C6/C2 → C3 ⊆ Aut C22×C12723(C2^2xC12).6C6288,76
(C22×C12).7C6 = C2×C4×C3.A4φ: C6/C2 → C3 ⊆ Aut C22×C1272(C2^2xC12).7C6288,343
(C22×C12).8C6 = A4×C24φ: C6/C2 → C3 ⊆ Aut C22×C12723(C2^2xC12).8C6288,637
(C22×C12).9C6 = C9×C2.C42φ: C6/C3 → C2 ⊆ Aut C22×C12288(C2^2xC12).9C6288,45
(C22×C12).10C6 = C9×C22⋊C8φ: C6/C3 → C2 ⊆ Aut C22×C12144(C2^2xC12).10C6288,48
(C22×C12).11C6 = C22⋊C4×C18φ: C6/C3 → C2 ⊆ Aut C22×C12144(C2^2xC12).11C6288,165
(C22×C12).12C6 = C4⋊C4×C18φ: C6/C3 → C2 ⊆ Aut C22×C12288(C2^2xC12).12C6288,166
(C22×C12).13C6 = D4×C36φ: C6/C3 → C2 ⊆ Aut C22×C12144(C2^2xC12).13C6288,168
(C22×C12).14C6 = C9×C22.D4φ: C6/C3 → C2 ⊆ Aut C22×C12144(C2^2xC12).14C6288,173
(C22×C12).15C6 = C3×C6.C42φ: C6/C3 → C2 ⊆ Aut C22×C1296(C2^2xC12).15C6288,265
(C22×C12).16C6 = C32×C2.C42φ: C6/C3 → C2 ⊆ Aut C22×C12288(C2^2xC12).16C6288,313
(C22×C12).17C6 = C32×C22⋊C8φ: C6/C3 → C2 ⊆ Aut C22×C12144(C2^2xC12).17C6288,316
(C22×C12).18C6 = C6×Dic3⋊C4φ: C6/C3 → C2 ⊆ Aut C22×C1296(C2^2xC12).18C6288,694
(C22×C12).19C6 = C3×C12.48D4φ: C6/C3 → C2 ⊆ Aut C22×C1248(C2^2xC12).19C6288,695
(C22×C12).20C6 = C6×C4⋊Dic3φ: C6/C3 → C2 ⊆ Aut C22×C1296(C2^2xC12).20C6288,696
(C22×C12).21C6 = C2×C6×Dic6φ: C6/C3 → C2 ⊆ Aut C22×C1296(C2^2xC12).21C6288,988
(C22×C12).22C6 = C6×C4.Dic3φ: C6/C3 → C2 ⊆ Aut C22×C1248(C2^2xC12).22C6288,692
(C22×C12).23C6 = C3×C23.26D6φ: C6/C3 → C2 ⊆ Aut C22×C1248(C2^2xC12).23C6288,697
(C22×C12).24C6 = C3×C12.55D4φ: C6/C3 → C2 ⊆ Aut C22×C1248(C2^2xC12).24C6288,264
(C22×C12).25C6 = C2×C6×C3⋊C8φ: C6/C3 → C2 ⊆ Aut C22×C1296(C2^2xC12).25C6288,691
(C22×C12).26C6 = Dic3×C2×C12φ: C6/C3 → C2 ⊆ Aut C22×C1296(C2^2xC12).26C6288,693
(C22×C12).27C6 = C9×C42⋊C2φ: C6/C3 → C2 ⊆ Aut C22×C12144(C2^2xC12).27C6288,167
(C22×C12).28C6 = C9×C4⋊D4φ: C6/C3 → C2 ⊆ Aut C22×C12144(C2^2xC12).28C6288,171
(C22×C12).29C6 = C9×C22⋊Q8φ: C6/C3 → C2 ⊆ Aut C22×C12144(C2^2xC12).29C6288,172
(C22×C12).30C6 = M4(2)×C18φ: C6/C3 → C2 ⊆ Aut C22×C12144(C2^2xC12).30C6288,180
(C22×C12).31C6 = D4×C2×C18φ: C6/C3 → C2 ⊆ Aut C22×C12144(C2^2xC12).31C6288,368
(C22×C12).32C6 = Q8×C2×C18φ: C6/C3 → C2 ⊆ Aut C22×C12288(C2^2xC12).32C6288,369
(C22×C12).33C6 = C4○D4×C18φ: C6/C3 → C2 ⊆ Aut C22×C12144(C2^2xC12).33C6288,370
(C22×C12).34C6 = C4⋊C4×C3×C6φ: C6/C3 → C2 ⊆ Aut C22×C12288(C2^2xC12).34C6288,813
(C22×C12).35C6 = C32×C42⋊C2φ: C6/C3 → C2 ⊆ Aut C22×C12144(C2^2xC12).35C6288,814
(C22×C12).36C6 = C32×C22⋊Q8φ: C6/C3 → C2 ⊆ Aut C22×C12144(C2^2xC12).36C6288,819
(C22×C12).37C6 = M4(2)×C3×C6φ: C6/C3 → C2 ⊆ Aut C22×C12144(C2^2xC12).37C6288,827
(C22×C12).38C6 = Q8×C62φ: C6/C3 → C2 ⊆ Aut C22×C12288(C2^2xC12).38C6288,1020

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