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

Direct product G=N×Q with N=C3×C6 and Q=C3×S3
dρLabelID
S3×C32×C6108S3xC3^2xC6324,172

Semidirect products G=N:Q with N=C3×C6 and Q=C3×S3
extensionφ:Q→Aut NdρLabelID
(C3×C6)⋊1(C3×S3) = C6×C32⋊C6φ: C3×S3/C3S3 ⊆ Aut C3×C6366(C3xC6):1(C3xS3)324,138
(C3×C6)⋊2(C3×S3) = C6×He3⋊C2φ: C3×S3/C3S3 ⊆ Aut C3×C654(C3xC6):2(C3xS3)324,145
(C3×C6)⋊3(C3×S3) = C2×He34S3φ: C3×S3/C3C6 ⊆ Aut C3×C654(C3xC6):3(C3xS3)324,144
(C3×C6)⋊4(C3×S3) = C2×S3×He3φ: C3×S3/S3C3 ⊆ Aut C3×C6366(C3xC6):4(C3xS3)324,139
(C3×C6)⋊5(C3×S3) = C3⋊S3×C3×C6φ: C3×S3/C32C2 ⊆ Aut C3×C636(C3xC6):5(C3xS3)324,173
(C3×C6)⋊6(C3×S3) = C6×C33⋊C2φ: C3×S3/C32C2 ⊆ Aut C3×C6108(C3xC6):6(C3xS3)324,174

Non-split extensions G=N.Q with N=C3×C6 and Q=C3×S3
extensionφ:Q→Aut NdρLabelID
(C3×C6).1(C3×S3) = He3⋊C12φ: C3×S3/C3S3 ⊆ Aut C3×C6363(C3xC6).1(C3xS3)324,13
(C3×C6).2(C3×S3) = He3.C12φ: C3×S3/C3S3 ⊆ Aut C3×C61083(C3xC6).2(C3xS3)324,15
(C3×C6).3(C3×S3) = He3.2C12φ: C3×S3/C3S3 ⊆ Aut C3×C61083(C3xC6).3(C3xS3)324,17
(C3×C6).4(C3×S3) = C2×C3≀S3φ: C3×S3/C3S3 ⊆ Aut C3×C6183(C3xC6).4(C3xS3)324,68
(C3×C6).5(C3×S3) = C2×He3.C6φ: C3×S3/C3S3 ⊆ Aut C3×C6543(C3xC6).5(C3xS3)324,70
(C3×C6).6(C3×S3) = C2×He3.2C6φ: C3×S3/C3S3 ⊆ Aut C3×C6543(C3xC6).6(C3xS3)324,72
(C3×C6).7(C3×S3) = C3×C32⋊C12φ: C3×S3/C3S3 ⊆ Aut C3×C6366(C3xC6).7(C3xS3)324,92
(C3×C6).8(C3×S3) = C3×C9⋊C12φ: C3×S3/C3S3 ⊆ Aut C3×C6366(C3xC6).8(C3xS3)324,94
(C3×C6).9(C3×S3) = C3×He33C4φ: C3×S3/C3S3 ⊆ Aut C3×C6108(C3xC6).9(C3xS3)324,99
(C3×C6).10(C3×S3) = He3.5C12φ: C3×S3/C3S3 ⊆ Aut C3×C61083(C3xC6).10(C3xS3)324,102
(C3×C6).11(C3×S3) = C6×C9⋊C6φ: C3×S3/C3S3 ⊆ Aut C3×C6366(C3xC6).11(C3xS3)324,140
(C3×C6).12(C3×S3) = C2×He3.4C6φ: C3×S3/C3S3 ⊆ Aut C3×C6543(C3xC6).12(C3xS3)324,148
(C3×C6).13(C3×S3) = C33⋊C12φ: C3×S3/C3C6 ⊆ Aut C3×C6366-(C3xC6).13(C3xS3)324,14
(C3×C6).14(C3×S3) = He3.Dic3φ: C3×S3/C3C6 ⊆ Aut C3×C61086-(C3xC6).14(C3xS3)324,16
(C3×C6).15(C3×S3) = He3.2Dic3φ: C3×S3/C3C6 ⊆ Aut C3×C61086-(C3xC6).15(C3xS3)324,18
(C3×C6).16(C3×S3) = C2×C33⋊C6φ: C3×S3/C3C6 ⊆ Aut C3×C6186+(C3xC6).16(C3xS3)324,69
(C3×C6).17(C3×S3) = C2×He3.S3φ: C3×S3/C3C6 ⊆ Aut C3×C6546+(C3xC6).17(C3xS3)324,71
(C3×C6).18(C3×S3) = C2×He3.2S3φ: C3×S3/C3C6 ⊆ Aut C3×C6546+(C3xC6).18(C3xS3)324,73
(C3×C6).19(C3×S3) = C334C12φ: C3×S3/C3C6 ⊆ Aut C3×C6108(C3xC6).19(C3xS3)324,98
(C3×C6).20(C3×S3) = He3.4Dic3φ: C3×S3/C3C6 ⊆ Aut C3×C61086-(C3xC6).20(C3xS3)324,101
(C3×C6).21(C3×S3) = C2×He3.4S3φ: C3×S3/C3C6 ⊆ Aut C3×C6546+(C3xC6).21(C3xS3)324,147
(C3×C6).22(C3×S3) = Dic3×He3φ: C3×S3/S3C3 ⊆ Aut C3×C6366(C3xC6).22(C3xS3)324,93
(C3×C6).23(C3×S3) = Dic3×3- 1+2φ: C3×S3/S3C3 ⊆ Aut C3×C6366(C3xC6).23(C3xS3)324,95
(C3×C6).24(C3×S3) = C2×S3×3- 1+2φ: C3×S3/S3C3 ⊆ Aut C3×C6366(C3xC6).24(C3xS3)324,141
(C3×C6).25(C3×S3) = C9×Dic9φ: C3×S3/C32C2 ⊆ Aut C3×C6362(C3xC6).25(C3xS3)324,6
(C3×C6).26(C3×S3) = C32⋊C36φ: C3×S3/C32C2 ⊆ Aut C3×C6366(C3xC6).26(C3xS3)324,7
(C3×C6).27(C3×S3) = C32⋊Dic9φ: C3×S3/C32C2 ⊆ Aut C3×C6108(C3xC6).27(C3xS3)324,8
(C3×C6).28(C3×S3) = C9⋊C36φ: C3×S3/C32C2 ⊆ Aut C3×C6366(C3xC6).28(C3xS3)324,9
(C3×C6).29(C3×S3) = D9×C18φ: C3×S3/C32C2 ⊆ Aut C3×C6362(C3xC6).29(C3xS3)324,61
(C3×C6).30(C3×S3) = C2×C32⋊C18φ: C3×S3/C32C2 ⊆ Aut C3×C6366(C3xC6).30(C3xS3)324,62
(C3×C6).31(C3×S3) = C2×C32⋊D9φ: C3×S3/C32C2 ⊆ Aut C3×C654(C3xC6).31(C3xS3)324,63
(C3×C6).32(C3×S3) = C2×C9⋊C18φ: C3×S3/C32C2 ⊆ Aut C3×C6366(C3xC6).32(C3xS3)324,64
(C3×C6).33(C3×S3) = C32×Dic9φ: C3×S3/C32C2 ⊆ Aut C3×C6108(C3xC6).33(C3xS3)324,90
(C3×C6).34(C3×S3) = C3×C9⋊Dic3φ: C3×S3/C32C2 ⊆ Aut C3×C6108(C3xC6).34(C3xS3)324,96
(C3×C6).35(C3×S3) = C9×C3⋊Dic3φ: C3×S3/C32C2 ⊆ Aut C3×C6108(C3xC6).35(C3xS3)324,97
(C3×C6).36(C3×S3) = C33.Dic3φ: C3×S3/C32C2 ⊆ Aut C3×C6108(C3xC6).36(C3xS3)324,100
(C3×C6).37(C3×S3) = D9×C3×C6φ: C3×S3/C32C2 ⊆ Aut C3×C6108(C3xC6).37(C3xS3)324,136
(C3×C6).38(C3×S3) = C6×C9⋊S3φ: C3×S3/C32C2 ⊆ Aut C3×C6108(C3xC6).38(C3xS3)324,142
(C3×C6).39(C3×S3) = C18×C3⋊S3φ: C3×S3/C32C2 ⊆ Aut C3×C6108(C3xC6).39(C3xS3)324,143
(C3×C6).40(C3×S3) = C2×C33.S3φ: C3×S3/C32C2 ⊆ Aut C3×C654(C3xC6).40(C3xS3)324,146
(C3×C6).41(C3×S3) = C32×C3⋊Dic3φ: C3×S3/C32C2 ⊆ Aut C3×C636(C3xC6).41(C3xS3)324,156
(C3×C6).42(C3×S3) = C3×C335C4φ: C3×S3/C32C2 ⊆ Aut C3×C6108(C3xC6).42(C3xS3)324,157
(C3×C6).43(C3×S3) = Dic3×C3×C9central extension (φ=1)108(C3xC6).43(C3xS3)324,91
(C3×C6).44(C3×S3) = S3×C3×C18central extension (φ=1)108(C3xC6).44(C3xS3)324,137
(C3×C6).45(C3×S3) = Dic3×C33central extension (φ=1)108(C3xC6).45(C3xS3)324,155

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