# Extensions 1→N→G→Q→1 with N=C24 and Q=C3×C6

Direct product G=N×Q with N=C24 and Q=C3×C6
dρLabelID
C3×C6×C24432C3xC6xC24432,515

Semidirect products G=N:Q with N=C24 and Q=C3×C6
extensionφ:Q→Aut NdρLabelID
C241(C3×C6) = C32×D24φ: C3×C6/C32C2 ⊆ Aut C24144C24:1(C3xC6)432,467
C242(C3×C6) = C32×C24⋊C2φ: C3×C6/C32C2 ⊆ Aut C24144C24:2(C3xC6)432,466
C243(C3×C6) = D8×C33φ: C3×C6/C32C2 ⊆ Aut C24216C24:3(C3xC6)432,517
C244(C3×C6) = S3×C3×C24φ: C3×C6/C32C2 ⊆ Aut C24144C24:4(C3xC6)432,464
C245(C3×C6) = C32×C8⋊S3φ: C3×C6/C32C2 ⊆ Aut C24144C24:5(C3xC6)432,465
C246(C3×C6) = SD16×C33φ: C3×C6/C32C2 ⊆ Aut C24216C24:6(C3xC6)432,518
C247(C3×C6) = M4(2)×C33φ: C3×C6/C32C2 ⊆ Aut C24216C24:7(C3xC6)432,516

Non-split extensions G=N.Q with N=C24 and Q=C3×C6
extensionφ:Q→Aut NdρLabelID
C24.1(C3×C6) = C32×Dic12φ: C3×C6/C32C2 ⊆ Aut C24144C24.1(C3xC6)432,468
C24.2(C3×C6) = D8×C3×C9φ: C3×C6/C32C2 ⊆ Aut C24216C24.2(C3xC6)432,215
C24.3(C3×C6) = D8×He3φ: C3×C6/C32C2 ⊆ Aut C24726C24.3(C3xC6)432,216
C24.4(C3×C6) = D8×3- 1+2φ: C3×C6/C32C2 ⊆ Aut C24726C24.4(C3xC6)432,217
C24.5(C3×C6) = Q16×C3×C9φ: C3×C6/C32C2 ⊆ Aut C24432C24.5(C3xC6)432,221
C24.6(C3×C6) = Q16×He3φ: C3×C6/C32C2 ⊆ Aut C241446C24.6(C3xC6)432,222
C24.7(C3×C6) = Q16×3- 1+2φ: C3×C6/C32C2 ⊆ Aut C241446C24.7(C3xC6)432,223
C24.8(C3×C6) = Q16×C33φ: C3×C6/C32C2 ⊆ Aut C24432C24.8(C3xC6)432,519
C24.9(C3×C6) = C32×C3⋊C16φ: C3×C6/C32C2 ⊆ Aut C24144C24.9(C3xC6)432,229
C24.10(C3×C6) = SD16×C3×C9φ: C3×C6/C32C2 ⊆ Aut C24216C24.10(C3xC6)432,218
C24.11(C3×C6) = SD16×He3φ: C3×C6/C32C2 ⊆ Aut C24726C24.11(C3xC6)432,219
C24.12(C3×C6) = SD16×3- 1+2φ: C3×C6/C32C2 ⊆ Aut C24726C24.12(C3xC6)432,220
C24.13(C3×C6) = M4(2)×C3×C9φ: C3×C6/C32C2 ⊆ Aut C24216C24.13(C3xC6)432,212
C24.14(C3×C6) = M4(2)×He3φ: C3×C6/C32C2 ⊆ Aut C24726C24.14(C3xC6)432,213
C24.15(C3×C6) = M4(2)×3- 1+2φ: C3×C6/C32C2 ⊆ Aut C24726C24.15(C3xC6)432,214
C24.16(C3×C6) = C16×He3central extension (φ=1)1443C24.16(C3xC6)432,35
C24.17(C3×C6) = C16×3- 1+2central extension (φ=1)1443C24.17(C3xC6)432,36
C24.18(C3×C6) = C2×C8×He3central extension (φ=1)144C24.18(C3xC6)432,210
C24.19(C3×C6) = C2×C8×3- 1+2central extension (φ=1)144C24.19(C3xC6)432,211

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