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

		d	ρ	Label	ID
C₃×C₆×C₂₄		432		C3xC6xC24	432,515

Semidirect products G=N:Q with N=C₂₄ and Q=C₃×C₆

extension	φ:Q→Aut N	d	ρ	Label	ID
C₂₄⋊₁(C₃×C₆) = C₃²×D₂₄	φ: C₃×C₆/C₃² → C₂ ⊆ Aut C₂₄	144		C24:1(C3xC6)	432,467
C₂₄⋊₂(C₃×C₆) = C₃²×C₂₄⋊C₂	φ: C₃×C₆/C₃² → C₂ ⊆ Aut C₂₄	144		C24:2(C3xC6)	432,466
C₂₄⋊₃(C₃×C₆) = D₈×C₃³	φ: C₃×C₆/C₃² → C₂ ⊆ Aut C₂₄	216		C24:3(C3xC6)	432,517
C₂₄⋊₄(C₃×C₆) = S₃×C₃×C₂₄	φ: C₃×C₆/C₃² → C₂ ⊆ Aut C₂₄	144		C24:4(C3xC6)	432,464
C₂₄⋊₅(C₃×C₆) = C₃²×C₈⋊S₃	φ: C₃×C₆/C₃² → C₂ ⊆ Aut C₂₄	144		C24:5(C3xC6)	432,465
C₂₄⋊₆(C₃×C₆) = SD₁₆×C₃³	φ: C₃×C₆/C₃² → C₂ ⊆ Aut C₂₄	216		C24:6(C3xC6)	432,518
C₂₄⋊₇(C₃×C₆) = M₄(2)×C₃³	φ: C₃×C₆/C₃² → C₂ ⊆ Aut C₂₄	216		C24:7(C3xC6)	432,516

Non-split extensions G=N.Q with N=C₂₄ and Q=C₃×C₆

extension	φ:Q→Aut N	d	ρ	Label	ID
C₂₄.₁(C₃×C₆) = C₃²×Dic₁₂	φ: C₃×C₆/C₃² → C₂ ⊆ Aut C₂₄	144		C24.1(C3xC6)	432,468
C₂₄.₂(C₃×C₆) = D₈×C₃×C₉	φ: C₃×C₆/C₃² → C₂ ⊆ Aut C₂₄	216		C24.2(C3xC6)	432,215
C₂₄.₃(C₃×C₆) = D₈×He₃	φ: C₃×C₆/C₃² → C₂ ⊆ Aut C₂₄	72	6	C24.3(C3xC6)	432,216
C₂₄.₄(C₃×C₆) = D₈×3_-¹⁺²	φ: C₃×C₆/C₃² → C₂ ⊆ Aut C₂₄	72	6	C24.4(C3xC6)	432,217
C₂₄.₅(C₃×C₆) = Q₁₆×C₃×C₉	φ: C₃×C₆/C₃² → C₂ ⊆ Aut C₂₄	432		C24.5(C3xC6)	432,221
C₂₄.₆(C₃×C₆) = Q₁₆×He₃	φ: C₃×C₆/C₃² → C₂ ⊆ Aut C₂₄	144	6	C24.6(C3xC6)	432,222
C₂₄.₇(C₃×C₆) = Q₁₆×3_-¹⁺²	φ: C₃×C₆/C₃² → C₂ ⊆ Aut C₂₄	144	6	C24.7(C3xC6)	432,223
C₂₄.₈(C₃×C₆) = Q₁₆×C₃³	φ: C₃×C₆/C₃² → C₂ ⊆ Aut C₂₄	432		C24.8(C3xC6)	432,519
C₂₄.₉(C₃×C₆) = C₃²×C₃⋊C₁₆	φ: C₃×C₆/C₃² → C₂ ⊆ Aut C₂₄	144		C24.9(C3xC6)	432,229
C₂₄.₁₀(C₃×C₆) = SD₁₆×C₃×C₉	φ: C₃×C₆/C₃² → C₂ ⊆ Aut C₂₄	216		C24.10(C3xC6)	432,218
C₂₄.₁₁(C₃×C₆) = SD₁₆×He₃	φ: C₃×C₆/C₃² → C₂ ⊆ Aut C₂₄	72	6	C24.11(C3xC6)	432,219
C₂₄.₁₂(C₃×C₆) = SD₁₆×3_-¹⁺²	φ: C₃×C₆/C₃² → C₂ ⊆ Aut C₂₄	72	6	C24.12(C3xC6)	432,220
C₂₄.₁₃(C₃×C₆) = M₄(2)×C₃×C₉	φ: C₃×C₆/C₃² → C₂ ⊆ Aut C₂₄	216		C24.13(C3xC6)	432,212
C₂₄.₁₄(C₃×C₆) = M₄(2)×He₃	φ: C₃×C₆/C₃² → C₂ ⊆ Aut C₂₄	72	6	C24.14(C3xC6)	432,213
C₂₄.₁₅(C₃×C₆) = M₄(2)×3_-¹⁺²	φ: C₃×C₆/C₃² → C₂ ⊆ Aut C₂₄	72	6	C24.15(C3xC6)	432,214
C₂₄.₁₆(C₃×C₆) = C₁₆×He₃	central extension (φ=1)	144	3	C24.16(C3xC6)	432,35
C₂₄.₁₇(C₃×C₆) = C₁₆×3_-¹⁺²	central extension (φ=1)	144	3	C24.17(C3xC6)	432,36
C₂₄.₁₈(C₃×C₆) = C₂×C₈×He₃	central extension (φ=1)	144		C24.18(C3xC6)	432,210
C₂₄.₁₉(C₃×C₆) = C₂×C₈×3_-¹⁺²	central extension (φ=1)	144		C24.19(C3xC6)	432,211

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