# Extensions 1→N→G→Q→1 with N=C33 and Q=C2×C6

Direct product G=N×Q with N=C33 and Q=C2×C6
dρLabelID
C32×C62324C3^2xC6^2324,176

Semidirect products G=N:Q with N=C33 and Q=C2×C6
extensionφ:Q→Aut NdρLabelID
C33⋊(C2×C6) = S3×C32⋊C6φ: C2×C6/C1C2×C6 ⊆ Aut C331812+C3^3:(C2xC6)324,116
C332(C2×C6) = C2×C33⋊C6φ: C2×C6/C2C6 ⊆ Aut C33186+C3^3:2(C2xC6)324,69
C333(C2×C6) = C6×C32⋊C6φ: C2×C6/C2C6 ⊆ Aut C33366C3^3:3(C2xC6)324,138
C334(C2×C6) = C2×S3×He3φ: C2×C6/C2C6 ⊆ Aut C33366C3^3:4(C2xC6)324,139
C335(C2×C6) = C2×He34S3φ: C2×C6/C2C6 ⊆ Aut C3354C3^3:5(C2xC6)324,144
C336(C2×C6) = S32×C32φ: C2×C6/C3C22 ⊆ Aut C3336C3^3:6(C2xC6)324,165
C337(C2×C6) = C3×S3×C3⋊S3φ: C2×C6/C3C22 ⊆ Aut C3336C3^3:7(C2xC6)324,166
C338(C2×C6) = C3×C324D6φ: C2×C6/C3C22 ⊆ Aut C33124C3^3:8(C2xC6)324,167
C339(C2×C6) = C22×C3≀C3φ: C2×C6/C22C3 ⊆ Aut C3336C3^3:9(C2xC6)324,86
C3310(C2×C6) = C2×C6×He3φ: C2×C6/C22C3 ⊆ Aut C33108C3^3:10(C2xC6)324,152
C3311(C2×C6) = S3×C32×C6φ: C2×C6/C6C2 ⊆ Aut C33108C3^3:11(C2xC6)324,172
C3312(C2×C6) = C3⋊S3×C3×C6φ: C2×C6/C6C2 ⊆ Aut C3336C3^3:12(C2xC6)324,173
C3313(C2×C6) = C6×C33⋊C2φ: C2×C6/C6C2 ⊆ Aut C33108C3^3:13(C2xC6)324,174

Non-split extensions G=N.Q with N=C33 and Q=C2×C6
extensionφ:Q→Aut NdρLabelID
C33.1(C2×C6) = C2×C32⋊C18φ: C2×C6/C2C6 ⊆ Aut C33366C3^3.1(C2xC6)324,62
C33.2(C2×C6) = C2×S3×3- 1+2φ: C2×C6/C2C6 ⊆ Aut C33366C3^3.2(C2xC6)324,141
C33.3(C2×C6) = S32×C9φ: C2×C6/C3C22 ⊆ Aut C33364C3^3.3(C2xC6)324,115
C33.4(C2×C6) = C22×C32⋊C9φ: C2×C6/C22C3 ⊆ Aut C33108C3^3.4(C2xC6)324,82
C33.5(C2×C6) = C2×C6×3- 1+2φ: C2×C6/C22C3 ⊆ Aut C33108C3^3.5(C2xC6)324,153
C33.6(C2×C6) = S3×C3×C18φ: C2×C6/C6C2 ⊆ Aut C33108C3^3.6(C2xC6)324,137
C33.7(C2×C6) = C18×C3⋊S3φ: C2×C6/C6C2 ⊆ Aut C33108C3^3.7(C2xC6)324,143

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