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Extensions 1→N→G→Q→1 with N=C24 and Q=C2×C6

Direct product G=N×Q with N=C24 and Q=C2×C6
dρLabelID
C2×C6×C24288C2xC6xC24288,826

Semidirect products G=N:Q with N=C24 and Q=C2×C6
extensionφ:Q→Aut NdρLabelID
C24⋊1(C2×C6) = C3×C8⋊D6φ: C2×C6/C3 → C22 ⊆ Aut C24484C24:1(C2xC6)288,679
C24⋊2(C2×C6) = C3×S3×D8φ: C2×C6/C3 → C22 ⊆ Aut C24484C24:2(C2xC6)288,681
C24⋊3(C2×C6) = C3×Q8⋊3D6φ: C2×C6/C3 → C22 ⊆ Aut C24484C24:3(C2xC6)288,685
C24⋊4(C2×C6) = C3×D8⋊S3φ: C2×C6/C3 → C22 ⊆ Aut C24484C24:4(C2xC6)288,682
C24⋊5(C2×C6) = C3×S3×SD16φ: C2×C6/C3 → C22 ⊆ Aut C24484C24:5(C2xC6)288,684
C24⋊6(C2×C6) = C32×C8⋊C22φ: C2×C6/C3 → C22 ⊆ Aut C2472C24:6(C2xC6)288,833
C24⋊7(C2×C6) = C3×S3×M4(2)φ: C2×C6/C3 → C22 ⊆ Aut C24484C24:7(C2xC6)288,677
C24⋊8(C2×C6) = C6×D24φ: C2×C6/C6 → C2 ⊆ Aut C2496C24:8(C2xC6)288,674
C24⋊9(C2×C6) = C6×C24⋊C2φ: C2×C6/C6 → C2 ⊆ Aut C2496C24:9(C2xC6)288,673
C24⋊10(C2×C6) = D8×C3×C6φ: C2×C6/C6 → C2 ⊆ Aut C24144C24:10(C2xC6)288,829
C24⋊11(C2×C6) = S3×C2×C24φ: C2×C6/C6 → C2 ⊆ Aut C2496C24:11(C2xC6)288,670
C24⋊12(C2×C6) = C6×C8⋊S3φ: C2×C6/C6 → C2 ⊆ Aut C2496C24:12(C2xC6)288,671
C24⋊13(C2×C6) = SD16×C3×C6φ: C2×C6/C6 → C2 ⊆ Aut C24144C24:13(C2xC6)288,830
C24⋊14(C2×C6) = M4(2)×C3×C6φ: C2×C6/C6 → C2 ⊆ Aut C24144C24:14(C2xC6)288,827

Non-split extensions G=N.Q with N=C24 and Q=C2×C6
extensionφ:Q→Aut NdρLabelID
C24.1(C2×C6) = C3×C8.D6φ: C2×C6/C3 → C22 ⊆ Aut C24484C24.1(C2xC6)288,680
C24.2(C2×C6) = C3×C3⋊D16φ: C2×C6/C3 → C22 ⊆ Aut C24484C24.2(C2xC6)288,260
C24.3(C2×C6) = C3×D8.S3φ: C2×C6/C3 → C22 ⊆ Aut C24484C24.3(C2xC6)288,261
C24.4(C2×C6) = C3×C8.6D6φ: C2×C6/C3 → C22 ⊆ Aut C24964C24.4(C2xC6)288,262
C24.5(C2×C6) = C3×C3⋊Q32φ: C2×C6/C3 → C22 ⊆ Aut C24964C24.5(C2xC6)288,263
C24.6(C2×C6) = C3×D8⋊3S3φ: C2×C6/C3 → C22 ⊆ Aut C24484C24.6(C2xC6)288,683
C24.7(C2×C6) = C3×S3×Q16φ: C2×C6/C3 → C22 ⊆ Aut C24964C24.7(C2xC6)288,688
C24.8(C2×C6) = C3×D24⋊C2φ: C2×C6/C3 → C22 ⊆ Aut C24964C24.8(C2xC6)288,690
C24.9(C2×C6) = C3×D4.D6φ: C2×C6/C3 → C22 ⊆ Aut C24484C24.9(C2xC6)288,686
C24.10(C2×C6) = C3×Q16⋊S3φ: C2×C6/C3 → C22 ⊆ Aut C24964C24.10(C2xC6)288,689
C24.11(C2×C6) = C3×Q8.7D6φ: C2×C6/C3 → C22 ⊆ Aut C24484C24.11(C2xC6)288,687
C24.12(C2×C6) = C9×C8⋊C22φ: C2×C6/C3 → C22 ⊆ Aut C24724C24.12(C2xC6)288,186
C24.13(C2×C6) = C9×C8.C22φ: C2×C6/C3 → C22 ⊆ Aut C241444C24.13(C2xC6)288,187
C24.14(C2×C6) = C32×C8.C22φ: C2×C6/C3 → C22 ⊆ Aut C24144C24.14(C2xC6)288,834
C24.15(C2×C6) = C3×D12.C4φ: C2×C6/C3 → C22 ⊆ Aut C24484C24.15(C2xC6)288,678
C24.16(C2×C6) = C3×D48φ: C2×C6/C6 → C2 ⊆ Aut C24962C24.16(C2xC6)288,233
C24.17(C2×C6) = C3×C48⋊C2φ: C2×C6/C6 → C2 ⊆ Aut C24962C24.17(C2xC6)288,234
C24.18(C2×C6) = C3×Dic24φ: C2×C6/C6 → C2 ⊆ Aut C24962C24.18(C2xC6)288,235
C24.19(C2×C6) = C3×C4○D24φ: C2×C6/C6 → C2 ⊆ Aut C24482C24.19(C2xC6)288,675
C24.20(C2×C6) = C6×Dic12φ: C2×C6/C6 → C2 ⊆ Aut C2496C24.20(C2xC6)288,676
C24.21(C2×C6) = C9×D16φ: C2×C6/C6 → C2 ⊆ Aut C241442C24.21(C2xC6)288,61
C24.22(C2×C6) = C9×SD32φ: C2×C6/C6 → C2 ⊆ Aut C241442C24.22(C2xC6)288,62
C24.23(C2×C6) = C9×Q32φ: C2×C6/C6 → C2 ⊆ Aut C242882C24.23(C2xC6)288,63
C24.24(C2×C6) = D8×C18φ: C2×C6/C6 → C2 ⊆ Aut C24144C24.24(C2xC6)288,182
C24.25(C2×C6) = Q16×C18φ: C2×C6/C6 → C2 ⊆ Aut C24288C24.25(C2xC6)288,184
C24.26(C2×C6) = C9×C4○D8φ: C2×C6/C6 → C2 ⊆ Aut C241442C24.26(C2xC6)288,185
C24.27(C2×C6) = C32×D16φ: C2×C6/C6 → C2 ⊆ Aut C24144C24.27(C2xC6)288,329
C24.28(C2×C6) = C32×SD32φ: C2×C6/C6 → C2 ⊆ Aut C24144C24.28(C2xC6)288,330
C24.29(C2×C6) = C32×Q32φ: C2×C6/C6 → C2 ⊆ Aut C24288C24.29(C2xC6)288,331
C24.30(C2×C6) = Q16×C3×C6φ: C2×C6/C6 → C2 ⊆ Aut C24288C24.30(C2xC6)288,831
C24.31(C2×C6) = C32×C4○D8φ: C2×C6/C6 → C2 ⊆ Aut C24144C24.31(C2xC6)288,832
C24.32(C2×C6) = S3×C48φ: C2×C6/C6 → C2 ⊆ Aut C24962C24.32(C2xC6)288,231
C24.33(C2×C6) = C3×D6.C8φ: C2×C6/C6 → C2 ⊆ Aut C24962C24.33(C2xC6)288,232
C24.34(C2×C6) = C6×C3⋊C16φ: C2×C6/C6 → C2 ⊆ Aut C2496C24.34(C2xC6)288,245
C24.35(C2×C6) = C3×C12.C8φ: C2×C6/C6 → C2 ⊆ Aut C24482C24.35(C2xC6)288,246
C24.36(C2×C6) = C3×C8○D12φ: C2×C6/C6 → C2 ⊆ Aut C24482C24.36(C2xC6)288,672
C24.37(C2×C6) = SD16×C18φ: C2×C6/C6 → C2 ⊆ Aut C24144C24.37(C2xC6)288,183
C24.38(C2×C6) = M4(2)×C18φ: C2×C6/C6 → C2 ⊆ Aut C24144C24.38(C2xC6)288,180
C24.39(C2×C6) = C9×C8○D4φ: C2×C6/C6 → C2 ⊆ Aut C241442C24.39(C2xC6)288,181
C24.40(C2×C6) = C32×C8○D4φ: C2×C6/C6 → C2 ⊆ Aut C24144C24.40(C2xC6)288,828
C24.41(C2×C6) = C9×M5(2)central extension (φ=1)1442C24.41(C2xC6)288,60
C24.42(C2×C6) = C32×M5(2)central extension (φ=1)144C24.42(C2xC6)288,328

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