Extensions 1→N→G→Q→1 with N=C₂² and Q=S₄

Direct product G=N×Q with N=C₂² and Q=S₄

		d	ρ	Label	ID
C₂²×S₄		12		C2^2xS4	96,226

Semidirect products G=N:Q with N=C₂² and Q=S₄

extension	φ:Q→Aut N	d	ρ	Label	ID
C₂²⋊S₄ = C₂²⋊S₄	φ: S₄/C₂² → S₃ ⊆ Aut C₂²	8	6+	C2^2:S4	96,227
C₂²⋊₂S₄ = A₄⋊D₄	φ: S₄/A₄ → C₂ ⊆ Aut C₂²	12	6+	C2^2:2S4	96,195

Non-split extensions G=N.Q with N=C₂² and Q=S₄

extension	φ:Q→Aut N	d	ρ	Label	ID
C₂².S₄ = C₄²⋊S₃	φ: S₄/C₂² → S₃ ⊆ Aut C₂²	12	3	C2^2.S4	96,64
C₂².₂S₄ = Q₈.D₆	φ: S₄/A₄ → C₂ ⊆ Aut C₂²	16	4-	C2^2.2S4	96,190
C₂².₃S₄ = Q₈⋊Dic₃	central extension (φ=1)	32		C2^2.3S4	96,66
C₂².₄S₄ = C₂×CSU₂(𝔽₃)	central extension (φ=1)	32		C2^2.4S4	96,188
C₂².₅S₄ = C₂×GL₂(𝔽₃)	central extension (φ=1)	16		C2^2.5S4	96,189
C₂².₆S₄ = C₂×A₄⋊C₄	central extension (φ=1)	24		C2^2.6S4	96,194

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