Extensions 1→N→G→Q→1 with N=C₂³ and Q=C₃²⋊C₄

Direct product G=N×Q with N=C₂³ and Q=C₃²⋊C₄

		d	ρ	Label	ID
C₂³×C₃²⋊C₄		48		C2^3xC3^2:C4	288,1039

Semidirect products G=N:Q with N=C₂³ and Q=C₃²⋊C₄

extension	φ:Q→Aut N	d	ρ	Label	ID
C₂³⋊(C₃²⋊C₄) = (C₂×C₆²)⋊C₄	φ: C₃²⋊C₄/C₃² → C₄ ⊆ Aut C₂³	24	4	C2^3:(C3^2:C4)	288,434
C₂³⋊₂(C₃²⋊C₄) = C₂×C₆²⋊C₄	φ: C₃²⋊C₄/C₃⋊S₃ → C₂ ⊆ Aut C₂³	24		C2^3:2(C3^2:C4)	288,941

Non-split extensions G=N.Q with N=C₂³ and Q=C₃²⋊C₄

extension	φ:Q→Aut N	d	ρ	Label	ID
C₂³.(C₃²⋊C₄) = (C₂×C₆²).C₄	φ: C₃²⋊C₄/C₃² → C₄ ⊆ Aut C₂³	24	4	C2^3.(C3^2:C4)	288,436
C₂³.₂(C₃²⋊C₄) = C₆²⋊₃C₈	φ: C₃²⋊C₄/C₃⋊S₃ → C₂ ⊆ Aut C₂³	48		C2^3.2(C3^2:C4)	288,435
C₂³.₃(C₃²⋊C₄) = C₂×C₆².C₄	φ: C₃²⋊C₄/C₃⋊S₃ → C₂ ⊆ Aut C₂³	48		C2^3.3(C3^2:C4)	288,940
C₂³.₄(C₃²⋊C₄) = C₂²×C₃²⋊₂C₈	central extension (φ=1)	96		C2^3.4(C3^2:C4)	288,939

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