# Extensions 1→N→G→Q→1 with N=C6 and Q=C22×C3⋊S3

Direct product G=N×Q with N=C6 and Q=C22×C3⋊S3
dρLabelID
C3⋊S3×C22×C6144C3:S3xC2^2xC6432,773

Semidirect products G=N:Q with N=C6 and Q=C22×C3⋊S3
extensionφ:Q→Aut NdρLabelID
C61(C22×C3⋊S3) = C22×S3×C3⋊S3φ: C22×C3⋊S3/C2×C3⋊S3C2 ⊆ Aut C672C6:1(C2^2xC3:S3)432,768
C62(C22×C3⋊S3) = C23×C33⋊C2φ: C22×C3⋊S3/C62C2 ⊆ Aut C6216C6:2(C2^2xC3:S3)432,774

Non-split extensions G=N.Q with N=C6 and Q=C22×C3⋊S3
extensionφ:Q→Aut NdρLabelID
C6.1(C22×C3⋊S3) = S3×C324Q8φ: C22×C3⋊S3/C2×C3⋊S3C2 ⊆ Aut C6144C6.1(C2^2xC3:S3)432,660
C6.2(C22×C3⋊S3) = (C3×D12)⋊S3φ: C22×C3⋊S3/C2×C3⋊S3C2 ⊆ Aut C6144C6.2(C2^2xC3:S3)432,661
C6.3(C22×C3⋊S3) = D12⋊(C3⋊S3)φ: C22×C3⋊S3/C2×C3⋊S3C2 ⊆ Aut C672C6.3(C2^2xC3:S3)432,662
C6.4(C22×C3⋊S3) = C3⋊S3×Dic6φ: C22×C3⋊S3/C2×C3⋊S3C2 ⊆ Aut C6144C6.4(C2^2xC3:S3)432,663
C6.5(C22×C3⋊S3) = C12.39S32φ: C22×C3⋊S3/C2×C3⋊S3C2 ⊆ Aut C672C6.5(C2^2xC3:S3)432,664
C6.6(C22×C3⋊S3) = C12.40S32φ: C22×C3⋊S3/C2×C3⋊S3C2 ⊆ Aut C672C6.6(C2^2xC3:S3)432,665
C6.7(C22×C3⋊S3) = C329(S3×Q8)φ: C22×C3⋊S3/C2×C3⋊S3C2 ⊆ Aut C672C6.7(C2^2xC3:S3)432,666
C6.8(C22×C3⋊S3) = C12.73S32φ: C22×C3⋊S3/C2×C3⋊S3C2 ⊆ Aut C672C6.8(C2^2xC3:S3)432,667
C6.9(C22×C3⋊S3) = C12.57S32φ: C22×C3⋊S3/C2×C3⋊S3C2 ⊆ Aut C6144C6.9(C2^2xC3:S3)432,668
C6.10(C22×C3⋊S3) = C12.58S32φ: C22×C3⋊S3/C2×C3⋊S3C2 ⊆ Aut C672C6.10(C2^2xC3:S3)432,669
C6.11(C22×C3⋊S3) = C4×S3×C3⋊S3φ: C22×C3⋊S3/C2×C3⋊S3C2 ⊆ Aut C672C6.11(C2^2xC3:S3)432,670
C6.12(C22×C3⋊S3) = S3×C12⋊S3φ: C22×C3⋊S3/C2×C3⋊S3C2 ⊆ Aut C672C6.12(C2^2xC3:S3)432,671
C6.13(C22×C3⋊S3) = C3⋊S3×D12φ: C22×C3⋊S3/C2×C3⋊S3C2 ⊆ Aut C672C6.13(C2^2xC3:S3)432,672
C6.14(C22×C3⋊S3) = C12⋊S32φ: C22×C3⋊S3/C2×C3⋊S3C2 ⊆ Aut C672C6.14(C2^2xC3:S3)432,673
C6.15(C22×C3⋊S3) = C2×S3×C3⋊Dic3φ: C22×C3⋊S3/C2×C3⋊S3C2 ⊆ Aut C6144C6.15(C2^2xC3:S3)432,674
C6.16(C22×C3⋊S3) = C62.90D6φ: C22×C3⋊S3/C2×C3⋊S3C2 ⊆ Aut C672C6.16(C2^2xC3:S3)432,675
C6.17(C22×C3⋊S3) = C62.91D6φ: C22×C3⋊S3/C2×C3⋊S3C2 ⊆ Aut C672C6.17(C2^2xC3:S3)432,676
C6.18(C22×C3⋊S3) = C2×Dic3×C3⋊S3φ: C22×C3⋊S3/C2×C3⋊S3C2 ⊆ Aut C6144C6.18(C2^2xC3:S3)432,677
C6.19(C22×C3⋊S3) = C62.93D6φ: C22×C3⋊S3/C2×C3⋊S3C2 ⊆ Aut C672C6.19(C2^2xC3:S3)432,678
C6.20(C22×C3⋊S3) = C2×C338(C2×C4)φ: C22×C3⋊S3/C2×C3⋊S3C2 ⊆ Aut C672C6.20(C2^2xC3:S3)432,679
C6.21(C22×C3⋊S3) = C2×C336D4φ: C22×C3⋊S3/C2×C3⋊S3C2 ⊆ Aut C6144C6.21(C2^2xC3:S3)432,680
C6.22(C22×C3⋊S3) = C2×C337D4φ: C22×C3⋊S3/C2×C3⋊S3C2 ⊆ Aut C672C6.22(C2^2xC3:S3)432,681
C6.23(C22×C3⋊S3) = C2×C338D4φ: C22×C3⋊S3/C2×C3⋊S3C2 ⊆ Aut C672C6.23(C2^2xC3:S3)432,682
C6.24(C22×C3⋊S3) = C2×C334Q8φ: C22×C3⋊S3/C2×C3⋊S3C2 ⊆ Aut C6144C6.24(C2^2xC3:S3)432,683
C6.25(C22×C3⋊S3) = S3×C327D4φ: C22×C3⋊S3/C2×C3⋊S3C2 ⊆ Aut C672C6.25(C2^2xC3:S3)432,684
C6.26(C22×C3⋊S3) = C3⋊S3×C3⋊D4φ: C22×C3⋊S3/C2×C3⋊S3C2 ⊆ Aut C672C6.26(C2^2xC3:S3)432,685
C6.27(C22×C3⋊S3) = C6223D6φ: C22×C3⋊S3/C2×C3⋊S3C2 ⊆ Aut C636C6.27(C2^2xC3:S3)432,686
C6.28(C22×C3⋊S3) = C2×C12.D9φ: C22×C3⋊S3/C62C2 ⊆ Aut C6432C6.28(C2^2xC3:S3)432,380
C6.29(C22×C3⋊S3) = C2×C4×C9⋊S3φ: C22×C3⋊S3/C62C2 ⊆ Aut C6216C6.29(C2^2xC3:S3)432,381
C6.30(C22×C3⋊S3) = C2×C36⋊S3φ: C22×C3⋊S3/C62C2 ⊆ Aut C6216C6.30(C2^2xC3:S3)432,382
C6.31(C22×C3⋊S3) = C36.70D6φ: C22×C3⋊S3/C62C2 ⊆ Aut C6216C6.31(C2^2xC3:S3)432,383
C6.32(C22×C3⋊S3) = D4×C9⋊S3φ: C22×C3⋊S3/C62C2 ⊆ Aut C6108C6.32(C2^2xC3:S3)432,388
C6.33(C22×C3⋊S3) = C36.27D6φ: C22×C3⋊S3/C62C2 ⊆ Aut C6216C6.33(C2^2xC3:S3)432,389
C6.34(C22×C3⋊S3) = Q8×C9⋊S3φ: C22×C3⋊S3/C62C2 ⊆ Aut C6216C6.34(C2^2xC3:S3)432,392
C6.35(C22×C3⋊S3) = C36.29D6φ: C22×C3⋊S3/C62C2 ⊆ Aut C6216C6.35(C2^2xC3:S3)432,393
C6.36(C22×C3⋊S3) = C22×C9⋊Dic3φ: C22×C3⋊S3/C62C2 ⊆ Aut C6432C6.36(C2^2xC3:S3)432,396
C6.37(C22×C3⋊S3) = C2×C6.D18φ: C22×C3⋊S3/C62C2 ⊆ Aut C6216C6.37(C2^2xC3:S3)432,397
C6.38(C22×C3⋊S3) = C23×C9⋊S3φ: C22×C3⋊S3/C62C2 ⊆ Aut C6216C6.38(C2^2xC3:S3)432,560
C6.39(C22×C3⋊S3) = C2×C338Q8φ: C22×C3⋊S3/C62C2 ⊆ Aut C6432C6.39(C2^2xC3:S3)432,720
C6.40(C22×C3⋊S3) = C2×C4×C33⋊C2φ: C22×C3⋊S3/C62C2 ⊆ Aut C6216C6.40(C2^2xC3:S3)432,721
C6.41(C22×C3⋊S3) = C2×C3312D4φ: C22×C3⋊S3/C62C2 ⊆ Aut C6216C6.41(C2^2xC3:S3)432,722
C6.42(C22×C3⋊S3) = C62.160D6φ: C22×C3⋊S3/C62C2 ⊆ Aut C6216C6.42(C2^2xC3:S3)432,723
C6.43(C22×C3⋊S3) = D4×C33⋊C2φ: C22×C3⋊S3/C62C2 ⊆ Aut C6108C6.43(C2^2xC3:S3)432,724
C6.44(C22×C3⋊S3) = C62.100D6φ: C22×C3⋊S3/C62C2 ⊆ Aut C6216C6.44(C2^2xC3:S3)432,725
C6.45(C22×C3⋊S3) = Q8×C33⋊C2φ: C22×C3⋊S3/C62C2 ⊆ Aut C6216C6.45(C2^2xC3:S3)432,726
C6.46(C22×C3⋊S3) = (Q8×C33)⋊C2φ: C22×C3⋊S3/C62C2 ⊆ Aut C6216C6.46(C2^2xC3:S3)432,727
C6.47(C22×C3⋊S3) = C22×C335C4φ: C22×C3⋊S3/C62C2 ⊆ Aut C6432C6.47(C2^2xC3:S3)432,728
C6.48(C22×C3⋊S3) = C2×C3315D4φ: C22×C3⋊S3/C62C2 ⊆ Aut C6216C6.48(C2^2xC3:S3)432,729
C6.49(C22×C3⋊S3) = C2×C4×He3⋊C2central extension (φ=1)72C6.49(C2^2xC3:S3)432,385
C6.50(C22×C3⋊S3) = C22×He33C4central extension (φ=1)144C6.50(C2^2xC3:S3)432,398
C6.51(C22×C3⋊S3) = C23×He3⋊C2central extension (φ=1)72C6.51(C2^2xC3:S3)432,561
C6.52(C22×C3⋊S3) = C6×C324Q8central extension (φ=1)144C6.52(C2^2xC3:S3)432,710
C6.53(C22×C3⋊S3) = C3⋊S3×C2×C12central extension (φ=1)144C6.53(C2^2xC3:S3)432,711
C6.54(C22×C3⋊S3) = C6×C12⋊S3central extension (φ=1)144C6.54(C2^2xC3:S3)432,712
C6.55(C22×C3⋊S3) = C3×C12.59D6central extension (φ=1)72C6.55(C2^2xC3:S3)432,713
C6.56(C22×C3⋊S3) = C3×D4×C3⋊S3central extension (φ=1)72C6.56(C2^2xC3:S3)432,714
C6.57(C22×C3⋊S3) = C3×C12.D6central extension (φ=1)72C6.57(C2^2xC3:S3)432,715
C6.58(C22×C3⋊S3) = C3×Q8×C3⋊S3central extension (φ=1)144C6.58(C2^2xC3:S3)432,716
C6.59(C22×C3⋊S3) = C3×C12.26D6central extension (φ=1)144C6.59(C2^2xC3:S3)432,717
C6.60(C22×C3⋊S3) = C2×C6×C3⋊Dic3central extension (φ=1)144C6.60(C2^2xC3:S3)432,718
C6.61(C22×C3⋊S3) = C6×C327D4central extension (φ=1)72C6.61(C2^2xC3:S3)432,719
C6.62(C22×C3⋊S3) = C2×He34Q8central stem extension (φ=1)144C6.62(C2^2xC3:S3)432,384
C6.63(C22×C3⋊S3) = C2×He35D4central stem extension (φ=1)72C6.63(C2^2xC3:S3)432,386
C6.64(C22×C3⋊S3) = C62.47D6central stem extension (φ=1)726C6.64(C2^2xC3:S3)432,387
C6.65(C22×C3⋊S3) = D4×He3⋊C2central stem extension (φ=1)366C6.65(C2^2xC3:S3)432,390
C6.66(C22×C3⋊S3) = C62.16D6central stem extension (φ=1)726C6.66(C2^2xC3:S3)432,391
C6.67(C22×C3⋊S3) = Q8×He3⋊C2central stem extension (φ=1)726C6.67(C2^2xC3:S3)432,394
C6.68(C22×C3⋊S3) = He35D4⋊C2central stem extension (φ=1)726C6.68(C2^2xC3:S3)432,395
C6.69(C22×C3⋊S3) = C2×He37D4central stem extension (φ=1)72C6.69(C2^2xC3:S3)432,399

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