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Extensions 1→N→G→Q→1 with N=C3×C6 and Q=C2×C6

Direct product G=N×Q with N=C3×C6 and Q=C2×C6
dρLabelID
C63216C6^3216,177

Semidirect products G=N:Q with N=C3×C6 and Q=C2×C6
extensionφ:Q→Aut NdρLabelID
(C3×C6)⋊(C2×C6) = C22×C32⋊C6φ: C2×C6/C2 → C6 ⊆ Aut C3×C636(C3xC6):(C2xC6)216,110
(C3×C6)⋊2(C2×C6) = S32×C6φ: C2×C6/C3 → C22 ⊆ Aut C3×C6244(C3xC6):2(C2xC6)216,170
(C3×C6)⋊3(C2×C6) = C23×He3φ: C2×C6/C22 → C3 ⊆ Aut C3×C672(C3xC6):3(C2xC6)216,115
(C3×C6)⋊4(C2×C6) = S3×C62φ: C2×C6/C6 → C2 ⊆ Aut C3×C672(C3xC6):4(C2xC6)216,174
(C3×C6)⋊5(C2×C6) = C2×C6×C3⋊S3φ: C2×C6/C6 → C2 ⊆ Aut C3×C672(C3xC6):5(C2xC6)216,175

Non-split extensions G=N.Q with N=C3×C6 and Q=C2×C6
extensionφ:Q→Aut NdρLabelID
(C3×C6).1(C2×C6) = He3⋊3Q8φ: C2×C6/C2 → C6 ⊆ Aut C3×C6726-(C3xC6).1(C2xC6)216,49
(C3×C6).2(C2×C6) = C4×C32⋊C6φ: C2×C6/C2 → C6 ⊆ Aut C3×C6366(C3xC6).2(C2xC6)216,50
(C3×C6).3(C2×C6) = He3⋊4D4φ: C2×C6/C2 → C6 ⊆ Aut C3×C6366+(C3xC6).3(C2xC6)216,51
(C3×C6).4(C2×C6) = C2×C32⋊C12φ: C2×C6/C2 → C6 ⊆ Aut C3×C672(C3xC6).4(C2xC6)216,59
(C3×C6).5(C2×C6) = He3⋊6D4φ: C2×C6/C2 → C6 ⊆ Aut C3×C6366(C3xC6).5(C2xC6)216,60
(C3×C6).6(C2×C6) = C3×S3×Dic3φ: C2×C6/C3 → C22 ⊆ Aut C3×C6244(C3xC6).6(C2xC6)216,119
(C3×C6).7(C2×C6) = C3×C6.D6φ: C2×C6/C3 → C22 ⊆ Aut C3×C6244(C3xC6).7(C2xC6)216,120
(C3×C6).8(C2×C6) = C3×D6⋊S3φ: C2×C6/C3 → C22 ⊆ Aut C3×C6244(C3xC6).8(C2xC6)216,121
(C3×C6).9(C2×C6) = C3×C3⋊D12φ: C2×C6/C3 → C22 ⊆ Aut C3×C6244(C3xC6).9(C2xC6)216,122
(C3×C6).10(C2×C6) = C3×C32⋊2Q8φ: C2×C6/C3 → C22 ⊆ Aut C3×C6244(C3xC6).10(C2xC6)216,123
(C3×C6).11(C2×C6) = C2×C4×He3φ: C2×C6/C22 → C3 ⊆ Aut C3×C672(C3xC6).11(C2xC6)216,74
(C3×C6).12(C2×C6) = C2×C4×3- 1+2φ: C2×C6/C22 → C3 ⊆ Aut C3×C672(C3xC6).12(C2xC6)216,75
(C3×C6).13(C2×C6) = D4×He3φ: C2×C6/C22 → C3 ⊆ Aut C3×C6366(C3xC6).13(C2xC6)216,77
(C3×C6).14(C2×C6) = D4×3- 1+2φ: C2×C6/C22 → C3 ⊆ Aut C3×C6366(C3xC6).14(C2xC6)216,78
(C3×C6).15(C2×C6) = Q8×He3φ: C2×C6/C22 → C3 ⊆ Aut C3×C6726(C3xC6).15(C2xC6)216,80
(C3×C6).16(C2×C6) = Q8×3- 1+2φ: C2×C6/C22 → C3 ⊆ Aut C3×C6726(C3xC6).16(C2xC6)216,81
(C3×C6).17(C2×C6) = C23×3- 1+2φ: C2×C6/C22 → C3 ⊆ Aut C3×C672(C3xC6).17(C2xC6)216,116
(C3×C6).18(C2×C6) = C9×Dic6φ: C2×C6/C6 → C2 ⊆ Aut C3×C6722(C3xC6).18(C2xC6)216,44
(C3×C6).19(C2×C6) = S3×C36φ: C2×C6/C6 → C2 ⊆ Aut C3×C6722(C3xC6).19(C2xC6)216,47
(C3×C6).20(C2×C6) = C9×D12φ: C2×C6/C6 → C2 ⊆ Aut C3×C6722(C3xC6).20(C2xC6)216,48
(C3×C6).21(C2×C6) = Dic3×C18φ: C2×C6/C6 → C2 ⊆ Aut C3×C672(C3xC6).21(C2xC6)216,56
(C3×C6).22(C2×C6) = C9×C3⋊D4φ: C2×C6/C6 → C2 ⊆ Aut C3×C6362(C3xC6).22(C2xC6)216,58
(C3×C6).23(C2×C6) = S3×C2×C18φ: C2×C6/C6 → C2 ⊆ Aut C3×C672(C3xC6).23(C2xC6)216,109
(C3×C6).24(C2×C6) = C32×Dic6φ: C2×C6/C6 → C2 ⊆ Aut C3×C672(C3xC6).24(C2xC6)216,135
(C3×C6).25(C2×C6) = S3×C3×C12φ: C2×C6/C6 → C2 ⊆ Aut C3×C672(C3xC6).25(C2xC6)216,136
(C3×C6).26(C2×C6) = C32×D12φ: C2×C6/C6 → C2 ⊆ Aut C3×C672(C3xC6).26(C2xC6)216,137
(C3×C6).27(C2×C6) = Dic3×C3×C6φ: C2×C6/C6 → C2 ⊆ Aut C3×C672(C3xC6).27(C2xC6)216,138
(C3×C6).28(C2×C6) = C32×C3⋊D4φ: C2×C6/C6 → C2 ⊆ Aut C3×C636(C3xC6).28(C2xC6)216,139
(C3×C6).29(C2×C6) = C3×C32⋊4Q8φ: C2×C6/C6 → C2 ⊆ Aut C3×C672(C3xC6).29(C2xC6)216,140
(C3×C6).30(C2×C6) = C12×C3⋊S3φ: C2×C6/C6 → C2 ⊆ Aut C3×C672(C3xC6).30(C2xC6)216,141
(C3×C6).31(C2×C6) = C3×C12⋊S3φ: C2×C6/C6 → C2 ⊆ Aut C3×C672(C3xC6).31(C2xC6)216,142
(C3×C6).32(C2×C6) = C6×C3⋊Dic3φ: C2×C6/C6 → C2 ⊆ Aut C3×C672(C3xC6).32(C2xC6)216,143
(C3×C6).33(C2×C6) = C3×C32⋊7D4φ: C2×C6/C6 → C2 ⊆ Aut C3×C636(C3xC6).33(C2xC6)216,144
(C3×C6).34(C2×C6) = D4×C3×C9central extension (φ=1)108(C3xC6).34(C2xC6)216,76
(C3×C6).35(C2×C6) = Q8×C3×C9central extension (φ=1)216(C3xC6).35(C2xC6)216,79
(C3×C6).36(C2×C6) = D4×C33central extension (φ=1)108(C3xC6).36(C2xC6)216,151
(C3×C6).37(C2×C6) = Q8×C33central extension (φ=1)216(C3xC6).37(C2xC6)216,152

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