Extensions 1→N→G→Q→1 with N=C₄ and Q=C₃²⋊₂Q₈

Direct product G=N×Q with N=C₄ and Q=C₃²⋊₂Q₈

		d	ρ	Label	ID
C₄×C₃²⋊₂Q₈		96		C4xC3^2:2Q8	288,565

Semidirect products G=N:Q with N=C₄ and Q=C₃²⋊₂Q₈

extension	φ:Q→Aut N	d	ρ	Label	ID
C₄⋊₁(C₃²⋊₂Q₈) = C₁₂⋊₃Dic₆	φ: C₃²⋊₂Q₈/C₃×Dic₃ → C₂ ⊆ Aut C₄	96		C4:1(C3^2:2Q8)	288,566
C₄⋊₂(C₃²⋊₂Q₈) = C₁₂⋊Dic₆	φ: C₃²⋊₂Q₈/C₃⋊Dic₃ → C₂ ⊆ Aut C₄	96		C4:2(C3^2:2Q8)	288,567

Non-split extensions G=N.Q with N=C₄ and Q=C₃²⋊₂Q₈

extension	φ:Q→Aut N	d	ρ	Label	ID
C₄.₁(C₃²⋊₂Q₈) = C₁₂.Dic₆	φ: C₃²⋊₂Q₈/C₃×Dic₃ → C₂ ⊆ Aut C₄	96		C4.1(C3^2:2Q8)	288,221
C₄.₂(C₃²⋊₂Q₈) = C₆.₁₈D₂₄	φ: C₃²⋊₂Q₈/C₃×Dic₃ → C₂ ⊆ Aut C₄	96		C4.2(C3^2:2Q8)	288,223
C₄.₃(C₃²⋊₂Q₈) = C₆².₃₉C₂³	φ: C₃²⋊₂Q₈/C₃×Dic₃ → C₂ ⊆ Aut C₄	96		C4.3(C3^2:2Q8)	288,517
C₄.₄(C₃²⋊₂Q₈) = C₁₂.₆Dic₆	φ: C₃²⋊₂Q₈/C₃⋊Dic₃ → C₂ ⊆ Aut C₄	96		C4.4(C3^2:2Q8)	288,222
C₄.₅(C₃²⋊₂Q₈) = C₁₂.₈Dic₆	φ: C₃²⋊₂Q₈/C₃⋊Dic₃ → C₂ ⊆ Aut C₄	96		C4.5(C3^2:2Q8)	288,224
C₄.₆(C₃²⋊₂Q₈) = C₆².₄₂C₂³	φ: C₃²⋊₂Q₈/C₃⋊Dic₃ → C₂ ⊆ Aut C₄	96		C4.6(C3^2:2Q8)	288,520
C₄.₇(C₃²⋊₂Q₈) = C₁₂.₈₁D₁₂	central extension (φ=1)	96		C4.7(C3^2:2Q8)	288,219
C₄.₈(C₃²⋊₂Q₈) = C₁₂.₁₅Dic₆	central extension (φ=1)	96		C4.8(C3^2:2Q8)	288,220

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