# Extensions 1→N→G→Q→1 with N=C23 and Q=S3×C6

Direct product G=N×Q with N=C23 and Q=S3×C6
dρLabelID
S3×C23×C696S3xC2^3xC6288,1043

Semidirect products G=N:Q with N=C23 and Q=S3×C6
extensionφ:Q→Aut NdρLabelID
C23⋊(S3×C6) = C2×C6×S4φ: S3×C6/C6S3 ⊆ Aut C2336C2^3:(S3xC6)288,1033
C232(S3×C6) = C3×C232D6φ: S3×C6/C32C22 ⊆ Aut C2348C2^3:2(S3xC6)288,708
C233(S3×C6) = C3×D46D6φ: S3×C6/C32C22 ⊆ Aut C23244C2^3:3(S3xC6)288,994
C234(S3×C6) = C22×S3×A4φ: S3×C6/D6C3 ⊆ Aut C2336C2^3:4(S3xC6)288,1037
C235(S3×C6) = S3×C6×D4φ: S3×C6/C3×S3C2 ⊆ Aut C2348C2^3:5(S3xC6)288,992
C236(S3×C6) = C2×C6×C3⋊D4φ: S3×C6/C3×C6C2 ⊆ Aut C2348C2^3:6(S3xC6)288,1002

Non-split extensions G=N.Q with N=C23 and Q=S3×C6
extensionφ:Q→Aut NdρLabelID
C23.1(S3×C6) = C3×A4⋊Q8φ: S3×C6/C6S3 ⊆ Aut C23726C2^3.1(S3xC6)288,896
C23.2(S3×C6) = C12×S4φ: S3×C6/C6S3 ⊆ Aut C23363C2^3.2(S3xC6)288,897
C23.3(S3×C6) = C3×C4⋊S4φ: S3×C6/C6S3 ⊆ Aut C23366C2^3.3(S3xC6)288,898
C23.4(S3×C6) = C6×A4⋊C4φ: S3×C6/C6S3 ⊆ Aut C2372C2^3.4(S3xC6)288,905
C23.5(S3×C6) = C3×A4⋊D4φ: S3×C6/C6S3 ⊆ Aut C23366C2^3.5(S3xC6)288,906
C23.6(S3×C6) = C3×C23.6D6φ: S3×C6/C32C22 ⊆ Aut C23244C2^3.6(S3xC6)288,240
C23.7(S3×C6) = C3×C23.7D6φ: S3×C6/C32C22 ⊆ Aut C23244C2^3.7(S3xC6)288,268
C23.8(S3×C6) = C3×C23.8D6φ: S3×C6/C32C22 ⊆ Aut C2348C2^3.8(S3xC6)288,650
C23.9(S3×C6) = C3×C23.9D6φ: S3×C6/C32C22 ⊆ Aut C2348C2^3.9(S3xC6)288,654
C23.10(S3×C6) = C3×Dic3⋊D4φ: S3×C6/C32C22 ⊆ Aut C2348C2^3.10(S3xC6)288,655
C23.11(S3×C6) = C3×C23.11D6φ: S3×C6/C32C22 ⊆ Aut C2348C2^3.11(S3xC6)288,656
C23.12(S3×C6) = C3×C23.12D6φ: S3×C6/C32C22 ⊆ Aut C2348C2^3.12(S3xC6)288,707
C23.13(S3×C6) = C3×D63D4φ: S3×C6/C32C22 ⊆ Aut C2348C2^3.13(S3xC6)288,709
C23.14(S3×C6) = C3×C23.14D6φ: S3×C6/C32C22 ⊆ Aut C2348C2^3.14(S3xC6)288,710
C23.15(S3×C6) = C3×C123D4φ: S3×C6/C32C22 ⊆ Aut C2348C2^3.15(S3xC6)288,711
C23.16(S3×C6) = A4×Dic6φ: S3×C6/D6C3 ⊆ Aut C23726-C2^3.16(S3xC6)288,918
C23.17(S3×C6) = C4×S3×A4φ: S3×C6/D6C3 ⊆ Aut C23366C2^3.17(S3xC6)288,919
C23.18(S3×C6) = A4×D12φ: S3×C6/D6C3 ⊆ Aut C23366+C2^3.18(S3xC6)288,920
C23.19(S3×C6) = C2×Dic3×A4φ: S3×C6/D6C3 ⊆ Aut C2372C2^3.19(S3xC6)288,927
C23.20(S3×C6) = A4×C3⋊D4φ: S3×C6/D6C3 ⊆ Aut C23366C2^3.20(S3xC6)288,928
C23.21(S3×C6) = C3×C23.16D6φ: S3×C6/C3×S3C2 ⊆ Aut C2348C2^3.21(S3xC6)288,648
C23.22(S3×C6) = C3×Dic3.D4φ: S3×C6/C3×S3C2 ⊆ Aut C2348C2^3.22(S3xC6)288,649
C23.23(S3×C6) = C3×S3×C22⋊C4φ: S3×C6/C3×S3C2 ⊆ Aut C2348C2^3.23(S3xC6)288,651
C23.24(S3×C6) = C3×Dic34D4φ: S3×C6/C3×S3C2 ⊆ Aut C2348C2^3.24(S3xC6)288,652
C23.25(S3×C6) = C3×D6⋊D4φ: S3×C6/C3×S3C2 ⊆ Aut C2348C2^3.25(S3xC6)288,653
C23.26(S3×C6) = C3×C23.21D6φ: S3×C6/C3×S3C2 ⊆ Aut C2348C2^3.26(S3xC6)288,657
C23.27(S3×C6) = C3×D4×Dic3φ: S3×C6/C3×S3C2 ⊆ Aut C2348C2^3.27(S3xC6)288,705
C23.28(S3×C6) = C3×C23.23D6φ: S3×C6/C3×S3C2 ⊆ Aut C2348C2^3.28(S3xC6)288,706
C23.29(S3×C6) = C6×D42S3φ: S3×C6/C3×S3C2 ⊆ Aut C2348C2^3.29(S3xC6)288,993
C23.30(S3×C6) = C3×C12.48D4φ: S3×C6/C3×C6C2 ⊆ Aut C2348C2^3.30(S3xC6)288,695
C23.31(S3×C6) = C3×C23.26D6φ: S3×C6/C3×C6C2 ⊆ Aut C2348C2^3.31(S3xC6)288,697
C23.32(S3×C6) = C12×C3⋊D4φ: S3×C6/C3×C6C2 ⊆ Aut C2348C2^3.32(S3xC6)288,699
C23.33(S3×C6) = C3×C23.28D6φ: S3×C6/C3×C6C2 ⊆ Aut C2348C2^3.33(S3xC6)288,700
C23.34(S3×C6) = C3×C127D4φ: S3×C6/C3×C6C2 ⊆ Aut C2348C2^3.34(S3xC6)288,701
C23.35(S3×C6) = C3×C244S3φ: S3×C6/C3×C6C2 ⊆ Aut C2324C2^3.35(S3xC6)288,724
C23.36(S3×C6) = C6×C4○D12φ: S3×C6/C3×C6C2 ⊆ Aut C2348C2^3.36(S3xC6)288,991
C23.37(S3×C6) = C3×C6.C42central extension (φ=1)96C2^3.37(S3xC6)288,265
C23.38(S3×C6) = Dic3×C2×C12central extension (φ=1)96C2^3.38(S3xC6)288,693
C23.39(S3×C6) = C6×Dic3⋊C4central extension (φ=1)96C2^3.39(S3xC6)288,694
C23.40(S3×C6) = C6×C4⋊Dic3central extension (φ=1)96C2^3.40(S3xC6)288,696
C23.41(S3×C6) = C6×D6⋊C4central extension (φ=1)96C2^3.41(S3xC6)288,698
C23.42(S3×C6) = C6×C6.D4central extension (φ=1)48C2^3.42(S3xC6)288,723
C23.43(S3×C6) = C2×C6×Dic6central extension (φ=1)96C2^3.43(S3xC6)288,988
C23.44(S3×C6) = S3×C22×C12central extension (φ=1)96C2^3.44(S3xC6)288,989
C23.45(S3×C6) = C2×C6×D12central extension (φ=1)96C2^3.45(S3xC6)288,990
C23.46(S3×C6) = Dic3×C22×C6central extension (φ=1)96C2^3.46(S3xC6)288,1001

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