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Extensions 1→N→G→Q→1 with N=C3×C6 and Q=C22×C6

Direct product G=N×Q with N=C3×C6 and Q=C22×C6
dρLabelID
C2×C63432C2xC6^3432,775

Semidirect products G=N:Q with N=C3×C6 and Q=C22×C6
extensionφ:Q→Aut NdρLabelID
(C3×C6)⋊(C22×C6) = C23×C32⋊C6φ: C22×C6/C22 → C6 ⊆ Aut C3×C672(C3xC6):(C2^2xC6)432,558
(C3×C6)⋊2(C22×C6) = S32×C2×C6φ: C22×C6/C6 → C22 ⊆ Aut C3×C648(C3xC6):2(C2^2xC6)432,767
(C3×C6)⋊3(C22×C6) = C24×He3φ: C22×C6/C23 → C3 ⊆ Aut C3×C6144(C3xC6):3(C2^2xC6)432,563
(C3×C6)⋊4(C22×C6) = S3×C2×C62φ: C22×C6/C2×C6 → C2 ⊆ Aut C3×C6144(C3xC6):4(C2^2xC6)432,772
(C3×C6)⋊5(C22×C6) = C3⋊S3×C22×C6φ: C22×C6/C2×C6 → C2 ⊆ Aut C3×C6144(C3xC6):5(C2^2xC6)432,773

Non-split extensions G=N.Q with N=C3×C6 and Q=C22×C6
extensionφ:Q→Aut NdρLabelID
(C3×C6).1(C22×C6) = C2×He3⋊3Q8φ: C22×C6/C22 → C6 ⊆ Aut C3×C6144(C3xC6).1(C2^2xC6)432,348
(C3×C6).2(C22×C6) = C2×C4×C32⋊C6φ: C22×C6/C22 → C6 ⊆ Aut C3×C672(C3xC6).2(C2^2xC6)432,349
(C3×C6).3(C22×C6) = C2×He3⋊4D4φ: C22×C6/C22 → C6 ⊆ Aut C3×C672(C3xC6).3(C2^2xC6)432,350
(C3×C6).4(C22×C6) = C62.36D6φ: C22×C6/C22 → C6 ⊆ Aut C3×C6726(C3xC6).4(C2^2xC6)432,351
(C3×C6).5(C22×C6) = D4×C32⋊C6φ: C22×C6/C22 → C6 ⊆ Aut C3×C63612+(C3xC6).5(C2^2xC6)432,360
(C3×C6).6(C22×C6) = C62.13D6φ: C22×C6/C22 → C6 ⊆ Aut C3×C67212-(C3xC6).6(C2^2xC6)432,361
(C3×C6).7(C22×C6) = Q8×C32⋊C6φ: C22×C6/C22 → C6 ⊆ Aut C3×C67212-(C3xC6).7(C2^2xC6)432,368
(C3×C6).8(C22×C6) = (Q8×He3)⋊C2φ: C22×C6/C22 → C6 ⊆ Aut C3×C67212+(C3xC6).8(C2^2xC6)432,369
(C3×C6).9(C22×C6) = C22×C32⋊C12φ: C22×C6/C22 → C6 ⊆ Aut C3×C6144(C3xC6).9(C2^2xC6)432,376
(C3×C6).10(C22×C6) = C2×He3⋊6D4φ: C22×C6/C22 → C6 ⊆ Aut C3×C672(C3xC6).10(C2^2xC6)432,377
(C3×C6).11(C22×C6) = C3×S3×Dic6φ: C22×C6/C6 → C22 ⊆ Aut C3×C6484(C3xC6).11(C2^2xC6)432,642
(C3×C6).12(C22×C6) = C3×D12⋊5S3φ: C22×C6/C6 → C22 ⊆ Aut C3×C6484(C3xC6).12(C2^2xC6)432,643
(C3×C6).13(C22×C6) = C3×D12⋊S3φ: C22×C6/C6 → C22 ⊆ Aut C3×C6484(C3xC6).13(C2^2xC6)432,644
(C3×C6).14(C22×C6) = C3×Dic3.D6φ: C22×C6/C6 → C22 ⊆ Aut C3×C6484(C3xC6).14(C2^2xC6)432,645
(C3×C6).15(C22×C6) = C3×D6.D6φ: C22×C6/C6 → C22 ⊆ Aut C3×C6484(C3xC6).15(C2^2xC6)432,646
(C3×C6).16(C22×C6) = C3×D6.6D6φ: C22×C6/C6 → C22 ⊆ Aut C3×C6484(C3xC6).16(C2^2xC6)432,647
(C3×C6).17(C22×C6) = S32×C12φ: C22×C6/C6 → C22 ⊆ Aut C3×C6484(C3xC6).17(C2^2xC6)432,648
(C3×C6).18(C22×C6) = C3×S3×D12φ: C22×C6/C6 → C22 ⊆ Aut C3×C6484(C3xC6).18(C2^2xC6)432,649
(C3×C6).19(C22×C6) = C3×D6⋊D6φ: C22×C6/C6 → C22 ⊆ Aut C3×C6484(C3xC6).19(C2^2xC6)432,650
(C3×C6).20(C22×C6) = S3×C6×Dic3φ: C22×C6/C6 → C22 ⊆ Aut C3×C648(C3xC6).20(C2^2xC6)432,651
(C3×C6).21(C22×C6) = C3×D6.3D6φ: C22×C6/C6 → C22 ⊆ Aut C3×C6244(C3xC6).21(C2^2xC6)432,652
(C3×C6).22(C22×C6) = C3×D6.4D6φ: C22×C6/C6 → C22 ⊆ Aut C3×C6244(C3xC6).22(C2^2xC6)432,653
(C3×C6).23(C22×C6) = C6×C6.D6φ: C22×C6/C6 → C22 ⊆ Aut C3×C648(C3xC6).23(C2^2xC6)432,654
(C3×C6).24(C22×C6) = C6×D6⋊S3φ: C22×C6/C6 → C22 ⊆ Aut C3×C648(C3xC6).24(C2^2xC6)432,655
(C3×C6).25(C22×C6) = C6×C3⋊D12φ: C22×C6/C6 → C22 ⊆ Aut C3×C648(C3xC6).25(C2^2xC6)432,656
(C3×C6).26(C22×C6) = C6×C32⋊2Q8φ: C22×C6/C6 → C22 ⊆ Aut C3×C648(C3xC6).26(C2^2xC6)432,657
(C3×C6).27(C22×C6) = C3×S3×C3⋊D4φ: C22×C6/C6 → C22 ⊆ Aut C3×C6244(C3xC6).27(C2^2xC6)432,658
(C3×C6).28(C22×C6) = C3×Dic3⋊D6φ: C22×C6/C6 → C22 ⊆ Aut C3×C6244(C3xC6).28(C2^2xC6)432,659
(C3×C6).29(C22×C6) = C22×C4×He3φ: C22×C6/C23 → C3 ⊆ Aut C3×C6144(C3xC6).29(C2^2xC6)432,401
(C3×C6).30(C22×C6) = C22×C4×3- 1+2φ: C22×C6/C23 → C3 ⊆ Aut C3×C6144(C3xC6).30(C2^2xC6)432,402
(C3×C6).31(C22×C6) = C2×D4×He3φ: C22×C6/C23 → C3 ⊆ Aut C3×C672(C3xC6).31(C2^2xC6)432,404
(C3×C6).32(C22×C6) = C2×D4×3- 1+2φ: C22×C6/C23 → C3 ⊆ Aut C3×C672(C3xC6).32(C2^2xC6)432,405
(C3×C6).33(C22×C6) = C2×Q8×He3φ: C22×C6/C23 → C3 ⊆ Aut C3×C6144(C3xC6).33(C2^2xC6)432,407
(C3×C6).34(C22×C6) = C2×Q8×3- 1+2φ: C22×C6/C23 → C3 ⊆ Aut C3×C6144(C3xC6).34(C2^2xC6)432,408
(C3×C6).35(C22×C6) = C4○D4×He3φ: C22×C6/C23 → C3 ⊆ Aut C3×C6726(C3xC6).35(C2^2xC6)432,410
(C3×C6).36(C22×C6) = C4○D4×3- 1+2φ: C22×C6/C23 → C3 ⊆ Aut C3×C6726(C3xC6).36(C2^2xC6)432,411
(C3×C6).37(C22×C6) = C24×3- 1+2φ: C22×C6/C23 → C3 ⊆ Aut C3×C6144(C3xC6).37(C2^2xC6)432,564
(C3×C6).38(C22×C6) = C18×Dic6φ: C22×C6/C2×C6 → C2 ⊆ Aut C3×C6144(C3xC6).38(C2^2xC6)432,341
(C3×C6).39(C22×C6) = S3×C2×C36φ: C22×C6/C2×C6 → C2 ⊆ Aut C3×C6144(C3xC6).39(C2^2xC6)432,345
(C3×C6).40(C22×C6) = C18×D12φ: C22×C6/C2×C6 → C2 ⊆ Aut C3×C6144(C3xC6).40(C2^2xC6)432,346
(C3×C6).41(C22×C6) = C9×C4○D12φ: C22×C6/C2×C6 → C2 ⊆ Aut C3×C6722(C3xC6).41(C2^2xC6)432,347
(C3×C6).42(C22×C6) = S3×D4×C9φ: C22×C6/C2×C6 → C2 ⊆ Aut C3×C6724(C3xC6).42(C2^2xC6)432,358
(C3×C6).43(C22×C6) = C9×D4⋊2S3φ: C22×C6/C2×C6 → C2 ⊆ Aut C3×C6724(C3xC6).43(C2^2xC6)432,359
(C3×C6).44(C22×C6) = S3×Q8×C9φ: C22×C6/C2×C6 → C2 ⊆ Aut C3×C61444(C3xC6).44(C2^2xC6)432,366
(C3×C6).45(C22×C6) = C9×Q8⋊3S3φ: C22×C6/C2×C6 → C2 ⊆ Aut C3×C61444(C3xC6).45(C2^2xC6)432,367
(C3×C6).46(C22×C6) = Dic3×C2×C18φ: C22×C6/C2×C6 → C2 ⊆ Aut C3×C6144(C3xC6).46(C2^2xC6)432,373
(C3×C6).47(C22×C6) = C18×C3⋊D4φ: C22×C6/C2×C6 → C2 ⊆ Aut C3×C672(C3xC6).47(C2^2xC6)432,375
(C3×C6).48(C22×C6) = S3×C22×C18φ: C22×C6/C2×C6 → C2 ⊆ Aut C3×C6144(C3xC6).48(C2^2xC6)432,557
(C3×C6).49(C22×C6) = C3×C6×Dic6φ: C22×C6/C2×C6 → C2 ⊆ Aut C3×C6144(C3xC6).49(C2^2xC6)432,700
(C3×C6).50(C22×C6) = S3×C6×C12φ: C22×C6/C2×C6 → C2 ⊆ Aut C3×C6144(C3xC6).50(C2^2xC6)432,701
(C3×C6).51(C22×C6) = C3×C6×D12φ: C22×C6/C2×C6 → C2 ⊆ Aut C3×C6144(C3xC6).51(C2^2xC6)432,702
(C3×C6).52(C22×C6) = C32×C4○D12φ: C22×C6/C2×C6 → C2 ⊆ Aut C3×C672(C3xC6).52(C2^2xC6)432,703
(C3×C6).53(C22×C6) = S3×D4×C32φ: C22×C6/C2×C6 → C2 ⊆ Aut C3×C672(C3xC6).53(C2^2xC6)432,704
(C3×C6).54(C22×C6) = C32×D4⋊2S3φ: C22×C6/C2×C6 → C2 ⊆ Aut C3×C672(C3xC6).54(C2^2xC6)432,705
(C3×C6).55(C22×C6) = S3×Q8×C32φ: C22×C6/C2×C6 → C2 ⊆ Aut C3×C6144(C3xC6).55(C2^2xC6)432,706
(C3×C6).56(C22×C6) = C32×Q8⋊3S3φ: C22×C6/C2×C6 → C2 ⊆ Aut C3×C6144(C3xC6).56(C2^2xC6)432,707
(C3×C6).57(C22×C6) = Dic3×C62φ: C22×C6/C2×C6 → C2 ⊆ Aut C3×C6144(C3xC6).57(C2^2xC6)432,708
(C3×C6).58(C22×C6) = C3×C6×C3⋊D4φ: C22×C6/C2×C6 → C2 ⊆ Aut C3×C672(C3xC6).58(C2^2xC6)432,709
(C3×C6).59(C22×C6) = C6×C32⋊4Q8φ: C22×C6/C2×C6 → C2 ⊆ Aut C3×C6144(C3xC6).59(C2^2xC6)432,710
(C3×C6).60(C22×C6) = C3⋊S3×C2×C12φ: C22×C6/C2×C6 → C2 ⊆ Aut C3×C6144(C3xC6).60(C2^2xC6)432,711
(C3×C6).61(C22×C6) = C6×C12⋊S3φ: C22×C6/C2×C6 → C2 ⊆ Aut C3×C6144(C3xC6).61(C2^2xC6)432,712
(C3×C6).62(C22×C6) = C3×C12.59D6φ: C22×C6/C2×C6 → C2 ⊆ Aut C3×C672(C3xC6).62(C2^2xC6)432,713
(C3×C6).63(C22×C6) = C3×D4×C3⋊S3φ: C22×C6/C2×C6 → C2 ⊆ Aut C3×C672(C3xC6).63(C2^2xC6)432,714
(C3×C6).64(C22×C6) = C3×C12.D6φ: C22×C6/C2×C6 → C2 ⊆ Aut C3×C672(C3xC6).64(C2^2xC6)432,715
(C3×C6).65(C22×C6) = C3×Q8×C3⋊S3φ: C22×C6/C2×C6 → C2 ⊆ Aut C3×C6144(C3xC6).65(C2^2xC6)432,716
(C3×C6).66(C22×C6) = C3×C12.26D6φ: C22×C6/C2×C6 → C2 ⊆ Aut C3×C6144(C3xC6).66(C2^2xC6)432,717
(C3×C6).67(C22×C6) = C2×C6×C3⋊Dic3φ: C22×C6/C2×C6 → C2 ⊆ Aut C3×C6144(C3xC6).67(C2^2xC6)432,718
(C3×C6).68(C22×C6) = C6×C32⋊7D4φ: C22×C6/C2×C6 → C2 ⊆ Aut C3×C672(C3xC6).68(C2^2xC6)432,719
(C3×C6).69(C22×C6) = D4×C3×C18central extension (φ=1)216(C3xC6).69(C2^2xC6)432,403
(C3×C6).70(C22×C6) = Q8×C3×C18central extension (φ=1)432(C3xC6).70(C2^2xC6)432,406
(C3×C6).71(C22×C6) = C4○D4×C3×C9central extension (φ=1)216(C3xC6).71(C2^2xC6)432,409
(C3×C6).72(C22×C6) = D4×C32×C6central extension (φ=1)216(C3xC6).72(C2^2xC6)432,731
(C3×C6).73(C22×C6) = Q8×C32×C6central extension (φ=1)432(C3xC6).73(C2^2xC6)432,732
(C3×C6).74(C22×C6) = C4○D4×C33central extension (φ=1)216(C3xC6).74(C2^2xC6)432,733

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