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

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

Semidirect products G=N:Q with N=C6 and Q=C2×C24
extensionφ:Q→Aut NdρLabelID
C61(C2×C24) = S3×C2×C24φ: C2×C24/C24C2 ⊆ Aut C696C6:1(C2xC24)288,670
C62(C2×C24) = C2×C6×C3⋊C8φ: C2×C24/C2×C12C2 ⊆ Aut C696C6:2(C2xC24)288,691

Non-split extensions G=N.Q with N=C6 and Q=C2×C24
extensionφ:Q→Aut NdρLabelID
C6.1(C2×C24) = S3×C48φ: C2×C24/C24C2 ⊆ Aut C6962C6.1(C2xC24)288,231
C6.2(C2×C24) = C3×D6.C8φ: C2×C24/C24C2 ⊆ Aut C6962C6.2(C2xC24)288,232
C6.3(C2×C24) = Dic3×C24φ: C2×C24/C24C2 ⊆ Aut C696C6.3(C2xC24)288,247
C6.4(C2×C24) = C3×Dic3⋊C8φ: C2×C24/C24C2 ⊆ Aut C696C6.4(C2xC24)288,248
C6.5(C2×C24) = C3×D6⋊C8φ: C2×C24/C24C2 ⊆ Aut C696C6.5(C2xC24)288,254
C6.6(C2×C24) = C12×C3⋊C8φ: C2×C24/C2×C12C2 ⊆ Aut C696C6.6(C2xC24)288,236
C6.7(C2×C24) = C3×C12⋊C8φ: C2×C24/C2×C12C2 ⊆ Aut C696C6.7(C2xC24)288,238
C6.8(C2×C24) = C6×C3⋊C16φ: C2×C24/C2×C12C2 ⊆ Aut C696C6.8(C2xC24)288,245
C6.9(C2×C24) = C3×C12.C8φ: C2×C24/C2×C12C2 ⊆ Aut C6482C6.9(C2xC24)288,246
C6.10(C2×C24) = C3×C12.55D4φ: C2×C24/C2×C12C2 ⊆ Aut C648C6.10(C2xC24)288,264
C6.11(C2×C24) = C9×C22⋊C8central extension (φ=1)144C6.11(C2xC24)288,48
C6.12(C2×C24) = C9×C4⋊C8central extension (φ=1)288C6.12(C2xC24)288,55
C6.13(C2×C24) = C9×M5(2)central extension (φ=1)1442C6.13(C2xC24)288,60
C6.14(C2×C24) = C32×C22⋊C8central extension (φ=1)144C6.14(C2xC24)288,316
C6.15(C2×C24) = C32×C4⋊C8central extension (φ=1)288C6.15(C2xC24)288,323
C6.16(C2×C24) = C32×M5(2)central extension (φ=1)144C6.16(C2xC24)288,328

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