Extensions 1→N→G→Q→1 with N=C₄ and Q=C₃²⋊₄Q₈

Direct product G=N×Q with N=C₄ and Q=C₃²⋊₄Q₈

		d	ρ	Label	ID
C₄×C₃²⋊₄Q₈		288		C4xC3^2:4Q8	288,725

Semidirect products G=N:Q with N=C₄ and Q=C₃²⋊₄Q₈

extension	φ:Q→Aut N	d	ρ	Label	ID
C₄⋊₁(C₃²⋊₄Q₈) = C₁₂⋊₂Dic₆	φ: C₃²⋊₄Q₈/C₃⋊Dic₃ → C₂ ⊆ Aut C₄	288		C4:1(C3^2:4Q8)	288,745
C₄⋊₂(C₃²⋊₄Q₈) = C₁₂⋊₆Dic₆	φ: C₃²⋊₄Q₈/C₃×C₁₂ → C₂ ⊆ Aut C₄	288		C4:2(C3^2:4Q8)	288,726

Non-split extensions G=N.Q with N=C₄ and Q=C₃²⋊₄Q₈

extension	φ:Q→Aut N	d	ρ	Label	ID
C₄.₁(C₃²⋊₄Q₈) = C₁₂.₉Dic₆	φ: C₃²⋊₄Q₈/C₃⋊Dic₃ → C₂ ⊆ Aut C₄	288		C4.1(C3^2:4Q8)	288,282
C₄.₂(C₃²⋊₄Q₈) = C₁₂.₁₀Dic₆	φ: C₃²⋊₄Q₈/C₃⋊Dic₃ → C₂ ⊆ Aut C₄	288		C4.2(C3^2:4Q8)	288,283
C₄.₃(C₃²⋊₄Q₈) = C₆².₂₃₄C₂³	φ: C₃²⋊₄Q₈/C₃⋊Dic₃ → C₂ ⊆ Aut C₄	288		C4.3(C3^2:4Q8)	288,747
C₄.₄(C₃²⋊₄Q₈) = C₂₄⋊₂Dic₃	φ: C₃²⋊₄Q₈/C₃×C₁₂ → C₂ ⊆ Aut C₄	288		C4.4(C3^2:4Q8)	288,292
C₄.₅(C₃²⋊₄Q₈) = C₂₄⋊₁Dic₃	φ: C₃²⋊₄Q₈/C₃×C₁₂ → C₂ ⊆ Aut C₄	288		C4.5(C3^2:4Q8)	288,293
C₄.₆(C₃²⋊₄Q₈) = C₁₂.₂₅Dic₆	φ: C₃²⋊₄Q₈/C₃×C₁₂ → C₂ ⊆ Aut C₄	288		C4.6(C3^2:4Q8)	288,727
C₄.₇(C₃²⋊₄Q₈) = C₁₂.₅₇D₁₂	central extension (φ=1)	288		C4.7(C3^2:4Q8)	288,279
C₄.₈(C₃²⋊₄Q₈) = C₁₂.₃₀Dic₆	central extension (φ=1)	288		C4.8(C3^2:4Q8)	288,289

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