Extensions 1→N→G→Q→1 with N=C₂³ and Q=A₄

Direct product G=N×Q with N=C₂³ and Q=A₄

		d	ρ	Label	ID
C₂³×A₄		24		C2^3xA4	96,228

Semidirect products G=N:Q with N=C₂³ and Q=A₄

extension	φ:Q→Aut N	d	ρ	Label	ID
C₂³⋊₁A₄ = C₂⁴⋊C₆	φ: A₄/C₁ → A₄ ⊆ Aut C₂³	8	6+	C2^3:1A4	96,70
C₂³⋊₂A₄ = C₂³⋊A₄	φ: A₄/C₁ → A₄ ⊆ Aut C₂³	8	4+	C2^3:2A4	96,204
C₂³⋊₃A₄ = C₂×C₂²⋊A₄	φ: A₄/C₂² → C₃ ⊆ Aut C₂³	12		C2^3:3A4	96,229

Non-split extensions G=N.Q with N=C₂³ and Q=A₄

extension	φ:Q→Aut N	d	ρ	Label	ID
C₂³.₁A₄ = C₄²⋊C₆	φ: A₄/C₁ → A₄ ⊆ Aut C₂³	16	6	C2^3.1A4	96,71
C₂³.₂A₄ = C₂³.A₄	φ: A₄/C₁ → A₄ ⊆ Aut C₂³	12	6+	C2^3.2A4	96,72
C₂³.₃A₄ = C₂³.₃A₄	φ: A₄/C₂² → C₃ ⊆ Aut C₂³	12	6+	C2^3.3A4	96,3
C₂³.₄A₄ = C₂×C₄²⋊C₃	φ: A₄/C₂² → C₃ ⊆ Aut C₂³	12	3	C2^3.4A4	96,68
C₂³.₅A₄ = Q₈⋊A₄	φ: A₄/C₂² → C₃ ⊆ Aut C₂³	24	6-	C2^3.5A4	96,203
C₂³.₆A₄ = C₂²×SL₂(𝔽₃)	central extension (φ=1)	32		C2^3.6A4	96,198

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