Extensions 1→N→G→Q→1 with N=C₄ and Q=C₃²⋊₄C₈

Direct product G=N×Q with N=C₄ and Q=C₃²⋊₄C₈

		d	ρ	Label	ID
C₄×C₃²⋊₄C₈		288		C4xC3^2:4C8	288,277

Semidirect products G=N:Q with N=C₄ and Q=C₃²⋊₄C₈

extension	φ:Q→Aut N	d	ρ	Label	ID
C₄⋊(C₃²⋊₄C₈) = C₁₂.₅₇D₁₂	φ: C₃²⋊₄C₈/C₃×C₁₂ → C₂ ⊆ Aut C₄	288		C4:(C3^2:4C8)	288,279

Non-split extensions G=N.Q with N=C₄ and Q=C₃²⋊₄C₈

extension	φ:Q→Aut N	d	Label	ID
C₄.(C₃²⋊₄C₈) = C₂₄.₉₄D₆	φ: C₃²⋊₄C₈/C₃×C₁₂ → C₂ ⊆ Aut C₄	144	C4.(C3^2:4C8)	288,287
C₄.₂(C₃²⋊₄C₈) = C₄₈.S₃	central extension (φ=1)	288	C4.2(C3^2:4C8)	288,65
C₄.₃(C₃²⋊₄C₈) = C₂×C₂₄.S₃	central extension (φ=1)	288	C4.3(C3^2:4C8)	288,286

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Extensions 1→N→G→Q→1 with N=C4 and Q=C32⋊4C8