# Extensions 1→N→G→Q→1 with N=C6 and Q=S3×C2×C6

Direct product G=N×Q with N=C6 and Q=S3×C2×C6
dρLabelID
S3×C2×C62144S3xC2xC6^2432,772

Semidirect products G=N:Q with N=C6 and Q=S3×C2×C6
extensionφ:Q→Aut NdρLabelID
C61(S3×C2×C6) = S32×C2×C6φ: S3×C2×C6/S3×C6C2 ⊆ Aut C648C6:1(S3xC2xC6)432,767
C62(S3×C2×C6) = C3⋊S3×C22×C6φ: S3×C2×C6/C62C2 ⊆ Aut C6144C6:2(S3xC2xC6)432,773

Non-split extensions G=N.Q with N=C6 and Q=S3×C2×C6
extensionφ:Q→Aut NdρLabelID
C6.1(S3×C2×C6) = C3×S3×Dic6φ: S3×C2×C6/S3×C6C2 ⊆ Aut C6484C6.1(S3xC2xC6)432,642
C6.2(S3×C2×C6) = C3×D125S3φ: S3×C2×C6/S3×C6C2 ⊆ Aut C6484C6.2(S3xC2xC6)432,643
C6.3(S3×C2×C6) = C3×D12⋊S3φ: S3×C2×C6/S3×C6C2 ⊆ Aut C6484C6.3(S3xC2xC6)432,644
C6.4(S3×C2×C6) = C3×Dic3.D6φ: S3×C2×C6/S3×C6C2 ⊆ Aut C6484C6.4(S3xC2xC6)432,645
C6.5(S3×C2×C6) = C3×D6.D6φ: S3×C2×C6/S3×C6C2 ⊆ Aut C6484C6.5(S3xC2xC6)432,646
C6.6(S3×C2×C6) = C3×D6.6D6φ: S3×C2×C6/S3×C6C2 ⊆ Aut C6484C6.6(S3xC2xC6)432,647
C6.7(S3×C2×C6) = S32×C12φ: S3×C2×C6/S3×C6C2 ⊆ Aut C6484C6.7(S3xC2xC6)432,648
C6.8(S3×C2×C6) = C3×S3×D12φ: S3×C2×C6/S3×C6C2 ⊆ Aut C6484C6.8(S3xC2xC6)432,649
C6.9(S3×C2×C6) = C3×D6⋊D6φ: S3×C2×C6/S3×C6C2 ⊆ Aut C6484C6.9(S3xC2xC6)432,650
C6.10(S3×C2×C6) = S3×C6×Dic3φ: S3×C2×C6/S3×C6C2 ⊆ Aut C648C6.10(S3xC2xC6)432,651
C6.11(S3×C2×C6) = C3×D6.3D6φ: S3×C2×C6/S3×C6C2 ⊆ Aut C6244C6.11(S3xC2xC6)432,652
C6.12(S3×C2×C6) = C3×D6.4D6φ: S3×C2×C6/S3×C6C2 ⊆ Aut C6244C6.12(S3xC2xC6)432,653
C6.13(S3×C2×C6) = C6×C6.D6φ: S3×C2×C6/S3×C6C2 ⊆ Aut C648C6.13(S3xC2xC6)432,654
C6.14(S3×C2×C6) = C6×D6⋊S3φ: S3×C2×C6/S3×C6C2 ⊆ Aut C648C6.14(S3xC2xC6)432,655
C6.15(S3×C2×C6) = C6×C3⋊D12φ: S3×C2×C6/S3×C6C2 ⊆ Aut C648C6.15(S3xC2xC6)432,656
C6.16(S3×C2×C6) = C6×C322Q8φ: S3×C2×C6/S3×C6C2 ⊆ Aut C648C6.16(S3xC2xC6)432,657
C6.17(S3×C2×C6) = C3×S3×C3⋊D4φ: S3×C2×C6/S3×C6C2 ⊆ Aut C6244C6.17(S3xC2xC6)432,658
C6.18(S3×C2×C6) = C3×Dic3⋊D6φ: S3×C2×C6/S3×C6C2 ⊆ Aut C6244C6.18(S3xC2xC6)432,659
C6.19(S3×C2×C6) = C6×Dic18φ: S3×C2×C6/C62C2 ⊆ Aut C6144C6.19(S3xC2xC6)432,340
C6.20(S3×C2×C6) = D9×C2×C12φ: S3×C2×C6/C62C2 ⊆ Aut C6144C6.20(S3xC2xC6)432,342
C6.21(S3×C2×C6) = C6×D36φ: S3×C2×C6/C62C2 ⊆ Aut C6144C6.21(S3xC2xC6)432,343
C6.22(S3×C2×C6) = C3×D365C2φ: S3×C2×C6/C62C2 ⊆ Aut C6722C6.22(S3xC2xC6)432,344
C6.23(S3×C2×C6) = C2×He33Q8φ: S3×C2×C6/C62C2 ⊆ Aut C6144C6.23(S3xC2xC6)432,348
C6.24(S3×C2×C6) = C2×C4×C32⋊C6φ: S3×C2×C6/C62C2 ⊆ Aut C672C6.24(S3xC2xC6)432,349
C6.25(S3×C2×C6) = C2×He34D4φ: S3×C2×C6/C62C2 ⊆ Aut C672C6.25(S3xC2xC6)432,350
C6.26(S3×C2×C6) = C62.36D6φ: S3×C2×C6/C62C2 ⊆ Aut C6726C6.26(S3xC2xC6)432,351
C6.27(S3×C2×C6) = C2×C36.C6φ: S3×C2×C6/C62C2 ⊆ Aut C6144C6.27(S3xC2xC6)432,352
C6.28(S3×C2×C6) = C2×C4×C9⋊C6φ: S3×C2×C6/C62C2 ⊆ Aut C672C6.28(S3xC2xC6)432,353
C6.29(S3×C2×C6) = C2×D36⋊C3φ: S3×C2×C6/C62C2 ⊆ Aut C672C6.29(S3xC2xC6)432,354
C6.30(S3×C2×C6) = D366C6φ: S3×C2×C6/C62C2 ⊆ Aut C6726C6.30(S3xC2xC6)432,355
C6.31(S3×C2×C6) = C3×D4×D9φ: S3×C2×C6/C62C2 ⊆ Aut C6724C6.31(S3xC2xC6)432,356
C6.32(S3×C2×C6) = C3×D42D9φ: S3×C2×C6/C62C2 ⊆ Aut C6724C6.32(S3xC2xC6)432,357
C6.33(S3×C2×C6) = D4×C32⋊C6φ: S3×C2×C6/C62C2 ⊆ Aut C63612+C6.33(S3xC2xC6)432,360
C6.34(S3×C2×C6) = C62.13D6φ: S3×C2×C6/C62C2 ⊆ Aut C67212-C6.34(S3xC2xC6)432,361
C6.35(S3×C2×C6) = D4×C9⋊C6φ: S3×C2×C6/C62C2 ⊆ Aut C63612+C6.35(S3xC2xC6)432,362
C6.36(S3×C2×C6) = Dic182C6φ: S3×C2×C6/C62C2 ⊆ Aut C67212-C6.36(S3xC2xC6)432,363
C6.37(S3×C2×C6) = C3×Q8×D9φ: S3×C2×C6/C62C2 ⊆ Aut C61444C6.37(S3xC2xC6)432,364
C6.38(S3×C2×C6) = C3×Q83D9φ: S3×C2×C6/C62C2 ⊆ Aut C61444C6.38(S3xC2xC6)432,365
C6.39(S3×C2×C6) = Q8×C32⋊C6φ: S3×C2×C6/C62C2 ⊆ Aut C67212-C6.39(S3xC2xC6)432,368
C6.40(S3×C2×C6) = (Q8×He3)⋊C2φ: S3×C2×C6/C62C2 ⊆ Aut C67212+C6.40(S3xC2xC6)432,369
C6.41(S3×C2×C6) = Q8×C9⋊C6φ: S3×C2×C6/C62C2 ⊆ Aut C67212-C6.41(S3xC2xC6)432,370
C6.42(S3×C2×C6) = D363C6φ: S3×C2×C6/C62C2 ⊆ Aut C67212+C6.42(S3xC2xC6)432,371
C6.43(S3×C2×C6) = C2×C6×Dic9φ: S3×C2×C6/C62C2 ⊆ Aut C6144C6.43(S3xC2xC6)432,372
C6.44(S3×C2×C6) = C6×C9⋊D4φ: S3×C2×C6/C62C2 ⊆ Aut C672C6.44(S3xC2xC6)432,374
C6.45(S3×C2×C6) = C22×C32⋊C12φ: S3×C2×C6/C62C2 ⊆ Aut C6144C6.45(S3xC2xC6)432,376
C6.46(S3×C2×C6) = C2×He36D4φ: S3×C2×C6/C62C2 ⊆ Aut C672C6.46(S3xC2xC6)432,377
C6.47(S3×C2×C6) = C22×C9⋊C12φ: S3×C2×C6/C62C2 ⊆ Aut C6144C6.47(S3xC2xC6)432,378
C6.48(S3×C2×C6) = C2×Dic9⋊C6φ: S3×C2×C6/C62C2 ⊆ Aut C672C6.48(S3xC2xC6)432,379
C6.49(S3×C2×C6) = D9×C22×C6φ: S3×C2×C6/C62C2 ⊆ Aut C6144C6.49(S3xC2xC6)432,556
C6.50(S3×C2×C6) = C23×C32⋊C6φ: S3×C2×C6/C62C2 ⊆ Aut C672C6.50(S3xC2xC6)432,558
C6.51(S3×C2×C6) = C23×C9⋊C6φ: S3×C2×C6/C62C2 ⊆ Aut C672C6.51(S3xC2xC6)432,559
C6.52(S3×C2×C6) = C6×C324Q8φ: S3×C2×C6/C62C2 ⊆ Aut C6144C6.52(S3xC2xC6)432,710
C6.53(S3×C2×C6) = C3⋊S3×C2×C12φ: S3×C2×C6/C62C2 ⊆ Aut C6144C6.53(S3xC2xC6)432,711
C6.54(S3×C2×C6) = C6×C12⋊S3φ: S3×C2×C6/C62C2 ⊆ Aut C6144C6.54(S3xC2xC6)432,712
C6.55(S3×C2×C6) = C3×C12.59D6φ: S3×C2×C6/C62C2 ⊆ Aut C672C6.55(S3xC2xC6)432,713
C6.56(S3×C2×C6) = C3×D4×C3⋊S3φ: S3×C2×C6/C62C2 ⊆ Aut C672C6.56(S3xC2xC6)432,714
C6.57(S3×C2×C6) = C3×C12.D6φ: S3×C2×C6/C62C2 ⊆ Aut C672C6.57(S3xC2xC6)432,715
C6.58(S3×C2×C6) = C3×Q8×C3⋊S3φ: S3×C2×C6/C62C2 ⊆ Aut C6144C6.58(S3xC2xC6)432,716
C6.59(S3×C2×C6) = C3×C12.26D6φ: S3×C2×C6/C62C2 ⊆ Aut C6144C6.59(S3xC2xC6)432,717
C6.60(S3×C2×C6) = C2×C6×C3⋊Dic3φ: S3×C2×C6/C62C2 ⊆ Aut C6144C6.60(S3xC2xC6)432,718
C6.61(S3×C2×C6) = C6×C327D4φ: S3×C2×C6/C62C2 ⊆ Aut C672C6.61(S3xC2xC6)432,719
C6.62(S3×C2×C6) = C18×Dic6central extension (φ=1)144C6.62(S3xC2xC6)432,341
C6.63(S3×C2×C6) = S3×C2×C36central extension (φ=1)144C6.63(S3xC2xC6)432,345
C6.64(S3×C2×C6) = C18×D12central extension (φ=1)144C6.64(S3xC2xC6)432,346
C6.65(S3×C2×C6) = C9×C4○D12central extension (φ=1)722C6.65(S3xC2xC6)432,347
C6.66(S3×C2×C6) = S3×D4×C9central extension (φ=1)724C6.66(S3xC2xC6)432,358
C6.67(S3×C2×C6) = C9×D42S3central extension (φ=1)724C6.67(S3xC2xC6)432,359
C6.68(S3×C2×C6) = S3×Q8×C9central extension (φ=1)1444C6.68(S3xC2xC6)432,366
C6.69(S3×C2×C6) = C9×Q83S3central extension (φ=1)1444C6.69(S3xC2xC6)432,367
C6.70(S3×C2×C6) = Dic3×C2×C18central extension (φ=1)144C6.70(S3xC2xC6)432,373
C6.71(S3×C2×C6) = C18×C3⋊D4central extension (φ=1)72C6.71(S3xC2xC6)432,375
C6.72(S3×C2×C6) = S3×C22×C18central extension (φ=1)144C6.72(S3xC2xC6)432,557
C6.73(S3×C2×C6) = C3×C6×Dic6central extension (φ=1)144C6.73(S3xC2xC6)432,700
C6.74(S3×C2×C6) = S3×C6×C12central extension (φ=1)144C6.74(S3xC2xC6)432,701
C6.75(S3×C2×C6) = C3×C6×D12central extension (φ=1)144C6.75(S3xC2xC6)432,702
C6.76(S3×C2×C6) = C32×C4○D12central extension (φ=1)72C6.76(S3xC2xC6)432,703
C6.77(S3×C2×C6) = S3×D4×C32central extension (φ=1)72C6.77(S3xC2xC6)432,704
C6.78(S3×C2×C6) = C32×D42S3central extension (φ=1)72C6.78(S3xC2xC6)432,705
C6.79(S3×C2×C6) = S3×Q8×C32central extension (φ=1)144C6.79(S3xC2xC6)432,706
C6.80(S3×C2×C6) = C32×Q83S3central extension (φ=1)144C6.80(S3xC2xC6)432,707
C6.81(S3×C2×C6) = Dic3×C62central extension (φ=1)144C6.81(S3xC2xC6)432,708
C6.82(S3×C2×C6) = C3×C6×C3⋊D4central extension (φ=1)72C6.82(S3xC2xC6)432,709

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