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

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

Semidirect products G=N:Q with N=C6 and Q=S3×C23
extensionφ:Q→Aut NdρLabelID
C61(S3×C23) = S32×C23φ: S3×C23/C22×S3C2 ⊆ Aut C648C6:1(S3xC2^3)288,1040
C62(S3×C23) = C24×C3⋊S3φ: S3×C23/C22×C6C2 ⊆ Aut C6144C6:2(S3xC2^3)288,1044

Non-split extensions G=N.Q with N=C6 and Q=S3×C23
extensionφ:Q→Aut NdρLabelID
C6.1(S3×C23) = C2×S3×Dic6φ: S3×C23/C22×S3C2 ⊆ Aut C696C6.1(S3xC2^3)288,942
C6.2(S3×C23) = C2×D125S3φ: S3×C23/C22×S3C2 ⊆ Aut C696C6.2(S3xC2^3)288,943
C6.3(S3×C23) = C2×D12⋊S3φ: S3×C23/C22×S3C2 ⊆ Aut C648C6.3(S3xC2^3)288,944
C6.4(S3×C23) = D12.33D6φ: S3×C23/C22×S3C2 ⊆ Aut C6484C6.4(S3xC2^3)288,945
C6.5(S3×C23) = D12.34D6φ: S3×C23/C22×S3C2 ⊆ Aut C6484-C6.5(S3xC2^3)288,946
C6.6(S3×C23) = C2×Dic3.D6φ: S3×C23/C22×S3C2 ⊆ Aut C648C6.6(S3xC2^3)288,947
C6.7(S3×C23) = C2×D6.D6φ: S3×C23/C22×S3C2 ⊆ Aut C648C6.7(S3xC2^3)288,948
C6.8(S3×C23) = C2×D6.6D6φ: S3×C23/C22×S3C2 ⊆ Aut C648C6.8(S3xC2^3)288,949
C6.9(S3×C23) = S32×C2×C4φ: S3×C23/C22×S3C2 ⊆ Aut C648C6.9(S3xC2^3)288,950
C6.10(S3×C23) = C2×S3×D12φ: S3×C23/C22×S3C2 ⊆ Aut C648C6.10(S3xC2^3)288,951
C6.11(S3×C23) = C2×D6⋊D6φ: S3×C23/C22×S3C2 ⊆ Aut C648C6.11(S3xC2^3)288,952
C6.12(S3×C23) = S3×C4○D12φ: S3×C23/C22×S3C2 ⊆ Aut C6484C6.12(S3xC2^3)288,953
C6.13(S3×C23) = D1223D6φ: S3×C23/C22×S3C2 ⊆ Aut C6244C6.13(S3xC2^3)288,954
C6.14(S3×C23) = D1224D6φ: S3×C23/C22×S3C2 ⊆ Aut C6484C6.14(S3xC2^3)288,955
C6.15(S3×C23) = D1227D6φ: S3×C23/C22×S3C2 ⊆ Aut C6244+C6.15(S3xC2^3)288,956
C6.16(S3×C23) = Dic6.24D6φ: S3×C23/C22×S3C2 ⊆ Aut C6488-C6.16(S3xC2^3)288,957
C6.17(S3×C23) = S32×D4φ: S3×C23/C22×S3C2 ⊆ Aut C6248+C6.17(S3xC2^3)288,958
C6.18(S3×C23) = S3×D42S3φ: S3×C23/C22×S3C2 ⊆ Aut C6488-C6.18(S3xC2^3)288,959
C6.19(S3×C23) = Dic612D6φ: S3×C23/C22×S3C2 ⊆ Aut C6248+C6.19(S3xC2^3)288,960
C6.20(S3×C23) = D1212D6φ: S3×C23/C22×S3C2 ⊆ Aut C6488-C6.20(S3xC2^3)288,961
C6.21(S3×C23) = D1213D6φ: S3×C23/C22×S3C2 ⊆ Aut C6248+C6.21(S3xC2^3)288,962
C6.22(S3×C23) = D12.25D6φ: S3×C23/C22×S3C2 ⊆ Aut C6488-C6.22(S3xC2^3)288,963
C6.23(S3×C23) = Dic6.26D6φ: S3×C23/C22×S3C2 ⊆ Aut C6488+C6.23(S3xC2^3)288,964
C6.24(S3×C23) = S32×Q8φ: S3×C23/C22×S3C2 ⊆ Aut C6488-C6.24(S3xC2^3)288,965
C6.25(S3×C23) = S3×Q83S3φ: S3×C23/C22×S3C2 ⊆ Aut C6488+C6.25(S3xC2^3)288,966
C6.26(S3×C23) = D1215D6φ: S3×C23/C22×S3C2 ⊆ Aut C6488-C6.26(S3xC2^3)288,967
C6.27(S3×C23) = D1216D6φ: S3×C23/C22×S3C2 ⊆ Aut C6488+C6.27(S3xC2^3)288,968
C6.28(S3×C23) = C22×S3×Dic3φ: S3×C23/C22×S3C2 ⊆ Aut C696C6.28(S3xC2^3)288,969
C6.29(S3×C23) = C2×D6.3D6φ: S3×C23/C22×S3C2 ⊆ Aut C648C6.29(S3xC2^3)288,970
C6.30(S3×C23) = C2×D6.4D6φ: S3×C23/C22×S3C2 ⊆ Aut C648C6.30(S3xC2^3)288,971
C6.31(S3×C23) = C22×C6.D6φ: S3×C23/C22×S3C2 ⊆ Aut C648C6.31(S3xC2^3)288,972
C6.32(S3×C23) = C22×D6⋊S3φ: S3×C23/C22×S3C2 ⊆ Aut C696C6.32(S3xC2^3)288,973
C6.33(S3×C23) = C22×C3⋊D12φ: S3×C23/C22×S3C2 ⊆ Aut C648C6.33(S3xC2^3)288,974
C6.34(S3×C23) = C22×C322Q8φ: S3×C23/C22×S3C2 ⊆ Aut C696C6.34(S3xC2^3)288,975
C6.35(S3×C23) = C2×S3×C3⋊D4φ: S3×C23/C22×S3C2 ⊆ Aut C648C6.35(S3xC2^3)288,976
C6.36(S3×C23) = C2×Dic3⋊D6φ: S3×C23/C22×S3C2 ⊆ Aut C624C6.36(S3xC2^3)288,977
C6.37(S3×C23) = C32⋊2+ 1+4φ: S3×C23/C22×S3C2 ⊆ Aut C6244C6.37(S3xC2^3)288,978
C6.38(S3×C23) = C22×Dic18φ: S3×C23/C22×C6C2 ⊆ Aut C6288C6.38(S3xC2^3)288,352
C6.39(S3×C23) = C22×C4×D9φ: S3×C23/C22×C6C2 ⊆ Aut C6144C6.39(S3xC2^3)288,353
C6.40(S3×C23) = C22×D36φ: S3×C23/C22×C6C2 ⊆ Aut C6144C6.40(S3xC2^3)288,354
C6.41(S3×C23) = C2×D365C2φ: S3×C23/C22×C6C2 ⊆ Aut C6144C6.41(S3xC2^3)288,355
C6.42(S3×C23) = C2×D4×D9φ: S3×C23/C22×C6C2 ⊆ Aut C672C6.42(S3xC2^3)288,356
C6.43(S3×C23) = C2×D42D9φ: S3×C23/C22×C6C2 ⊆ Aut C6144C6.43(S3xC2^3)288,357
C6.44(S3×C23) = D46D18φ: S3×C23/C22×C6C2 ⊆ Aut C6724C6.44(S3xC2^3)288,358
C6.45(S3×C23) = C2×Q8×D9φ: S3×C23/C22×C6C2 ⊆ Aut C6144C6.45(S3xC2^3)288,359
C6.46(S3×C23) = C2×Q83D9φ: S3×C23/C22×C6C2 ⊆ Aut C6144C6.46(S3xC2^3)288,360
C6.47(S3×C23) = Q8.15D18φ: S3×C23/C22×C6C2 ⊆ Aut C61444C6.47(S3xC2^3)288,361
C6.48(S3×C23) = C4○D4×D9φ: S3×C23/C22×C6C2 ⊆ Aut C6724C6.48(S3xC2^3)288,362
C6.49(S3×C23) = D48D18φ: S3×C23/C22×C6C2 ⊆ Aut C6724+C6.49(S3xC2^3)288,363
C6.50(S3×C23) = D4.10D18φ: S3×C23/C22×C6C2 ⊆ Aut C61444-C6.50(S3xC2^3)288,364
C6.51(S3×C23) = C23×Dic9φ: S3×C23/C22×C6C2 ⊆ Aut C6288C6.51(S3xC2^3)288,365
C6.52(S3×C23) = C22×C9⋊D4φ: S3×C23/C22×C6C2 ⊆ Aut C6144C6.52(S3xC2^3)288,366
C6.53(S3×C23) = C24×D9φ: S3×C23/C22×C6C2 ⊆ Aut C6144C6.53(S3xC2^3)288,839
C6.54(S3×C23) = C22×C324Q8φ: S3×C23/C22×C6C2 ⊆ Aut C6288C6.54(S3xC2^3)288,1003
C6.55(S3×C23) = C22×C4×C3⋊S3φ: S3×C23/C22×C6C2 ⊆ Aut C6144C6.55(S3xC2^3)288,1004
C6.56(S3×C23) = C22×C12⋊S3φ: S3×C23/C22×C6C2 ⊆ Aut C6144C6.56(S3xC2^3)288,1005
C6.57(S3×C23) = C2×C12.59D6φ: S3×C23/C22×C6C2 ⊆ Aut C6144C6.57(S3xC2^3)288,1006
C6.58(S3×C23) = C2×D4×C3⋊S3φ: S3×C23/C22×C6C2 ⊆ Aut C672C6.58(S3xC2^3)288,1007
C6.59(S3×C23) = C2×C12.D6φ: S3×C23/C22×C6C2 ⊆ Aut C6144C6.59(S3xC2^3)288,1008
C6.60(S3×C23) = C3282+ 1+4φ: S3×C23/C22×C6C2 ⊆ Aut C672C6.60(S3xC2^3)288,1009
C6.61(S3×C23) = C2×Q8×C3⋊S3φ: S3×C23/C22×C6C2 ⊆ Aut C6144C6.61(S3xC2^3)288,1010
C6.62(S3×C23) = C2×C12.26D6φ: S3×C23/C22×C6C2 ⊆ Aut C6144C6.62(S3xC2^3)288,1011
C6.63(S3×C23) = C3272- 1+4φ: S3×C23/C22×C6C2 ⊆ Aut C6144C6.63(S3xC2^3)288,1012
C6.64(S3×C23) = C4○D4×C3⋊S3φ: S3×C23/C22×C6C2 ⊆ Aut C672C6.64(S3xC2^3)288,1013
C6.65(S3×C23) = C62.154C23φ: S3×C23/C22×C6C2 ⊆ Aut C672C6.65(S3xC2^3)288,1014
C6.66(S3×C23) = C3292- 1+4φ: S3×C23/C22×C6C2 ⊆ Aut C6144C6.66(S3xC2^3)288,1015
C6.67(S3×C23) = C23×C3⋊Dic3φ: S3×C23/C22×C6C2 ⊆ Aut C6288C6.67(S3xC2^3)288,1016
C6.68(S3×C23) = C22×C327D4φ: S3×C23/C22×C6C2 ⊆ Aut C6144C6.68(S3xC2^3)288,1017
C6.69(S3×C23) = C2×C6×Dic6central extension (φ=1)96C6.69(S3xC2^3)288,988
C6.70(S3×C23) = S3×C22×C12central extension (φ=1)96C6.70(S3xC2^3)288,989
C6.71(S3×C23) = C2×C6×D12central extension (φ=1)96C6.71(S3xC2^3)288,990
C6.72(S3×C23) = C6×C4○D12central extension (φ=1)48C6.72(S3xC2^3)288,991
C6.73(S3×C23) = S3×C6×D4central extension (φ=1)48C6.73(S3xC2^3)288,992
C6.74(S3×C23) = C6×D42S3central extension (φ=1)48C6.74(S3xC2^3)288,993
C6.75(S3×C23) = C3×D46D6central extension (φ=1)244C6.75(S3xC2^3)288,994
C6.76(S3×C23) = S3×C6×Q8central extension (φ=1)96C6.76(S3xC2^3)288,995
C6.77(S3×C23) = C6×Q83S3central extension (φ=1)96C6.77(S3xC2^3)288,996
C6.78(S3×C23) = C3×Q8.15D6central extension (φ=1)484C6.78(S3xC2^3)288,997
C6.79(S3×C23) = C3×S3×C4○D4central extension (φ=1)484C6.79(S3xC2^3)288,998
C6.80(S3×C23) = C3×D4○D12central extension (φ=1)484C6.80(S3xC2^3)288,999
C6.81(S3×C23) = C3×Q8○D12central extension (φ=1)484C6.81(S3xC2^3)288,1000
C6.82(S3×C23) = Dic3×C22×C6central extension (φ=1)96C6.82(S3xC2^3)288,1001
C6.83(S3×C23) = C2×C6×C3⋊D4central extension (φ=1)48C6.83(S3xC2^3)288,1002

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