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Extensions 1→N→G→Q→1 with N=C12 and Q=C2×C4

Direct product G=N×Q with N=C12 and Q=C2×C4
dρLabelID
C2×C4×C1296C2xC4xC1296,161

Semidirect products G=N:Q with N=C12 and Q=C2×C4
extensionφ:Q→Aut NdρLabelID
C12⋊1(C2×C4) = S3×C4⋊C4φ: C2×C4/C2 → C22 ⊆ Aut C1248C12:1(C2xC4)96,98
C12⋊2(C2×C4) = Dic3⋊5D4φ: C2×C4/C2 → C22 ⊆ Aut C1248C12:2(C2xC4)96,100
C12⋊3(C2×C4) = D4×Dic3φ: C2×C4/C2 → C22 ⊆ Aut C1248C12:3(C2xC4)96,141
C12⋊4(C2×C4) = C4×D12φ: C2×C4/C4 → C2 ⊆ Aut C1248C12:4(C2xC4)96,80
C12⋊5(C2×C4) = S3×C42φ: C2×C4/C4 → C2 ⊆ Aut C1248C12:5(C2xC4)96,78
C12⋊6(C2×C4) = D4×C12φ: C2×C4/C4 → C2 ⊆ Aut C1248C12:6(C2xC4)96,165
C12⋊7(C2×C4) = C2×C4⋊Dic3φ: C2×C4/C22 → C2 ⊆ Aut C1296C12:7(C2xC4)96,132
C12⋊8(C2×C4) = C2×C4×Dic3φ: C2×C4/C22 → C2 ⊆ Aut C1296C12:8(C2xC4)96,129
C12⋊9(C2×C4) = C6×C4⋊C4φ: C2×C4/C22 → C2 ⊆ Aut C1296C12:9(C2xC4)96,163

Non-split extensions G=N.Q with N=C12 and Q=C2×C4
extensionφ:Q→Aut NdρLabelID
C12.1(C2×C4) = C6.Q16φ: C2×C4/C2 → C22 ⊆ Aut C1296C12.1(C2xC4)96,14
C12.2(C2×C4) = C12.Q8φ: C2×C4/C2 → C22 ⊆ Aut C1296C12.2(C2xC4)96,15
C12.3(C2×C4) = C6.D8φ: C2×C4/C2 → C22 ⊆ Aut C1248C12.3(C2xC4)96,16
C12.4(C2×C4) = C6.SD16φ: C2×C4/C2 → C22 ⊆ Aut C1296C12.4(C2xC4)96,17
C12.5(C2×C4) = C12.53D4φ: C2×C4/C2 → C22 ⊆ Aut C12484C12.5(C2xC4)96,29
C12.6(C2×C4) = D12⋊C4φ: C2×C4/C2 → C22 ⊆ Aut C12244C12.6(C2xC4)96,32
C12.7(C2×C4) = D4⋊Dic3φ: C2×C4/C2 → C22 ⊆ Aut C1248C12.7(C2xC4)96,39
C12.8(C2×C4) = Q8⋊2Dic3φ: C2×C4/C2 → C22 ⊆ Aut C1296C12.8(C2xC4)96,42
C12.9(C2×C4) = Q8⋊3Dic3φ: C2×C4/C2 → C22 ⊆ Aut C12244C12.9(C2xC4)96,44
C12.10(C2×C4) = Dic6⋊C4φ: C2×C4/C2 → C22 ⊆ Aut C1296C12.10(C2xC4)96,94
C12.11(C2×C4) = C4⋊C4⋊7S3φ: C2×C4/C2 → C22 ⊆ Aut C1248C12.11(C2xC4)96,99
C12.12(C2×C4) = S3×M4(2)φ: C2×C4/C2 → C22 ⊆ Aut C12244C12.12(C2xC4)96,113
C12.13(C2×C4) = D12.C4φ: C2×C4/C2 → C22 ⊆ Aut C12484C12.13(C2xC4)96,114
C12.14(C2×C4) = Q8×Dic3φ: C2×C4/C2 → C22 ⊆ Aut C1296C12.14(C2xC4)96,152
C12.15(C2×C4) = D4.Dic3φ: C2×C4/C2 → C22 ⊆ Aut C12484C12.15(C2xC4)96,155
C12.16(C2×C4) = C42⋊4S3φ: C2×C4/C4 → C2 ⊆ Aut C12242C12.16(C2xC4)96,12
C12.17(C2×C4) = C2.Dic12φ: C2×C4/C4 → C2 ⊆ Aut C1296C12.17(C2xC4)96,23
C12.18(C2×C4) = C2.D24φ: C2×C4/C4 → C2 ⊆ Aut C1248C12.18(C2xC4)96,28
C12.19(C2×C4) = C4×Dic6φ: C2×C4/C4 → C2 ⊆ Aut C1296C12.19(C2xC4)96,75
C12.20(C2×C4) = C8○D12φ: C2×C4/C4 → C2 ⊆ Aut C12482C12.20(C2xC4)96,108
C12.21(C2×C4) = S3×C16φ: C2×C4/C4 → C2 ⊆ Aut C12482C12.21(C2xC4)96,4
C12.22(C2×C4) = D6.C8φ: C2×C4/C4 → C2 ⊆ Aut C12482C12.22(C2xC4)96,5
C12.23(C2×C4) = C4×C3⋊C8φ: C2×C4/C4 → C2 ⊆ Aut C1296C12.23(C2xC4)96,9
C12.24(C2×C4) = C42.S3φ: C2×C4/C4 → C2 ⊆ Aut C1296C12.24(C2xC4)96,10
C12.25(C2×C4) = C42⋊2S3φ: C2×C4/C4 → C2 ⊆ Aut C1248C12.25(C2xC4)96,79
C12.26(C2×C4) = S3×C2×C8φ: C2×C4/C4 → C2 ⊆ Aut C1248C12.26(C2xC4)96,106
C12.27(C2×C4) = C2×C8⋊S3φ: C2×C4/C4 → C2 ⊆ Aut C1248C12.27(C2xC4)96,107
C12.28(C2×C4) = C3×D4⋊C4φ: C2×C4/C4 → C2 ⊆ Aut C1248C12.28(C2xC4)96,52
C12.29(C2×C4) = C3×Q8⋊C4φ: C2×C4/C4 → C2 ⊆ Aut C1296C12.29(C2xC4)96,53
C12.30(C2×C4) = C3×C4≀C2φ: C2×C4/C4 → C2 ⊆ Aut C12242C12.30(C2xC4)96,54
C12.31(C2×C4) = Q8×C12φ: C2×C4/C4 → C2 ⊆ Aut C1296C12.31(C2xC4)96,166
C12.32(C2×C4) = C3×C8○D4φ: C2×C4/C4 → C2 ⊆ Aut C12482C12.32(C2xC4)96,178
C12.33(C2×C4) = C8⋊Dic3φ: C2×C4/C22 → C2 ⊆ Aut C1296C12.33(C2xC4)96,24
C12.34(C2×C4) = C24⋊1C4φ: C2×C4/C22 → C2 ⊆ Aut C1296C12.34(C2xC4)96,25
C12.35(C2×C4) = C24.C4φ: C2×C4/C22 → C2 ⊆ Aut C12482C12.35(C2xC4)96,26
C12.36(C2×C4) = C2×C4.Dic3φ: C2×C4/C22 → C2 ⊆ Aut C1248C12.36(C2xC4)96,128
C12.37(C2×C4) = C23.26D6φ: C2×C4/C22 → C2 ⊆ Aut C1248C12.37(C2xC4)96,133
C12.38(C2×C4) = C2×C3⋊C16φ: C2×C4/C22 → C2 ⊆ Aut C1296C12.38(C2xC4)96,18
C12.39(C2×C4) = C12.C8φ: C2×C4/C22 → C2 ⊆ Aut C12482C12.39(C2xC4)96,19
C12.40(C2×C4) = C8×Dic3φ: C2×C4/C22 → C2 ⊆ Aut C1296C12.40(C2xC4)96,20
C12.41(C2×C4) = C24⋊C4φ: C2×C4/C22 → C2 ⊆ Aut C1296C12.41(C2xC4)96,22
C12.42(C2×C4) = C22×C3⋊C8φ: C2×C4/C22 → C2 ⊆ Aut C1296C12.42(C2xC4)96,127
C12.43(C2×C4) = C3×C4.Q8φ: C2×C4/C22 → C2 ⊆ Aut C1296C12.43(C2xC4)96,56
C12.44(C2×C4) = C3×C2.D8φ: C2×C4/C22 → C2 ⊆ Aut C1296C12.44(C2xC4)96,57
C12.45(C2×C4) = C3×C8.C4φ: C2×C4/C22 → C2 ⊆ Aut C12482C12.45(C2xC4)96,58
C12.46(C2×C4) = C3×C42⋊C2φ: C2×C4/C22 → C2 ⊆ Aut C1248C12.46(C2xC4)96,164
C12.47(C2×C4) = C6×M4(2)φ: C2×C4/C22 → C2 ⊆ Aut C1248C12.47(C2xC4)96,177
C12.48(C2×C4) = C3×C8⋊C4central extension (φ=1)96C12.48(C2xC4)96,47
C12.49(C2×C4) = C3×M5(2)central extension (φ=1)482C12.49(C2xC4)96,60

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