# Extensions 1→N→G→Q→1 with N=C6 and Q=C22×C4

Direct product G=N×Q with N=C6 and Q=C22×C4
dρLabelID
C23×C1296C2^3xC1296,220

Semidirect products G=N:Q with N=C6 and Q=C22×C4
extensionφ:Q→Aut NdρLabelID
C61(C22×C4) = S3×C22×C4φ: C22×C4/C2×C4C2 ⊆ Aut C648C6:1(C2^2xC4)96,206
C62(C22×C4) = C23×Dic3φ: C22×C4/C23C2 ⊆ Aut C696C6:2(C2^2xC4)96,218

Non-split extensions G=N.Q with N=C6 and Q=C22×C4
extensionφ:Q→Aut NdρLabelID
C6.1(C22×C4) = C4×Dic6φ: C22×C4/C2×C4C2 ⊆ Aut C696C6.1(C2^2xC4)96,75
C6.2(C22×C4) = S3×C42φ: C22×C4/C2×C4C2 ⊆ Aut C648C6.2(C2^2xC4)96,78
C6.3(C22×C4) = C422S3φ: C22×C4/C2×C4C2 ⊆ Aut C648C6.3(C2^2xC4)96,79
C6.4(C22×C4) = C4×D12φ: C22×C4/C2×C4C2 ⊆ Aut C648C6.4(C2^2xC4)96,80
C6.5(C22×C4) = C23.16D6φ: C22×C4/C2×C4C2 ⊆ Aut C648C6.5(C2^2xC4)96,84
C6.6(C22×C4) = S3×C22⋊C4φ: C22×C4/C2×C4C2 ⊆ Aut C624C6.6(C2^2xC4)96,87
C6.7(C22×C4) = Dic34D4φ: C22×C4/C2×C4C2 ⊆ Aut C648C6.7(C2^2xC4)96,88
C6.8(C22×C4) = Dic6⋊C4φ: C22×C4/C2×C4C2 ⊆ Aut C696C6.8(C2^2xC4)96,94
C6.9(C22×C4) = S3×C4⋊C4φ: C22×C4/C2×C4C2 ⊆ Aut C648C6.9(C2^2xC4)96,98
C6.10(C22×C4) = C4⋊C47S3φ: C22×C4/C2×C4C2 ⊆ Aut C648C6.10(C2^2xC4)96,99
C6.11(C22×C4) = Dic35D4φ: C22×C4/C2×C4C2 ⊆ Aut C648C6.11(C2^2xC4)96,100
C6.12(C22×C4) = S3×C2×C8φ: C22×C4/C2×C4C2 ⊆ Aut C648C6.12(C2^2xC4)96,106
C6.13(C22×C4) = C2×C8⋊S3φ: C22×C4/C2×C4C2 ⊆ Aut C648C6.13(C2^2xC4)96,107
C6.14(C22×C4) = C8○D12φ: C22×C4/C2×C4C2 ⊆ Aut C6482C6.14(C2^2xC4)96,108
C6.15(C22×C4) = S3×M4(2)φ: C22×C4/C2×C4C2 ⊆ Aut C6244C6.15(C2^2xC4)96,113
C6.16(C22×C4) = D12.C4φ: C22×C4/C2×C4C2 ⊆ Aut C6484C6.16(C2^2xC4)96,114
C6.17(C22×C4) = C2×Dic3⋊C4φ: C22×C4/C2×C4C2 ⊆ Aut C696C6.17(C2^2xC4)96,130
C6.18(C22×C4) = C2×D6⋊C4φ: C22×C4/C2×C4C2 ⊆ Aut C648C6.18(C2^2xC4)96,134
C6.19(C22×C4) = C4×C3⋊D4φ: C22×C4/C2×C4C2 ⊆ Aut C648C6.19(C2^2xC4)96,135
C6.20(C22×C4) = C22×C3⋊C8φ: C22×C4/C23C2 ⊆ Aut C696C6.20(C2^2xC4)96,127
C6.21(C22×C4) = C2×C4.Dic3φ: C22×C4/C23C2 ⊆ Aut C648C6.21(C2^2xC4)96,128
C6.22(C22×C4) = C2×C4×Dic3φ: C22×C4/C23C2 ⊆ Aut C696C6.22(C2^2xC4)96,129
C6.23(C22×C4) = C2×C4⋊Dic3φ: C22×C4/C23C2 ⊆ Aut C696C6.23(C2^2xC4)96,132
C6.24(C22×C4) = C23.26D6φ: C22×C4/C23C2 ⊆ Aut C648C6.24(C2^2xC4)96,133
C6.25(C22×C4) = D4×Dic3φ: C22×C4/C23C2 ⊆ Aut C648C6.25(C2^2xC4)96,141
C6.26(C22×C4) = Q8×Dic3φ: C22×C4/C23C2 ⊆ Aut C696C6.26(C2^2xC4)96,152
C6.27(C22×C4) = D4.Dic3φ: C22×C4/C23C2 ⊆ Aut C6484C6.27(C2^2xC4)96,155
C6.28(C22×C4) = C2×C6.D4φ: C22×C4/C23C2 ⊆ Aut C648C6.28(C2^2xC4)96,159
C6.29(C22×C4) = C6×C22⋊C4central extension (φ=1)48C6.29(C2^2xC4)96,162
C6.30(C22×C4) = C6×C4⋊C4central extension (φ=1)96C6.30(C2^2xC4)96,163
C6.31(C22×C4) = C3×C42⋊C2central extension (φ=1)48C6.31(C2^2xC4)96,164
C6.32(C22×C4) = D4×C12central extension (φ=1)48C6.32(C2^2xC4)96,165
C6.33(C22×C4) = Q8×C12central extension (φ=1)96C6.33(C2^2xC4)96,166
C6.34(C22×C4) = C6×M4(2)central extension (φ=1)48C6.34(C2^2xC4)96,177
C6.35(C22×C4) = C3×C8○D4central extension (φ=1)482C6.35(C2^2xC4)96,178

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