Extensions 1→N→G→Q→1 with N=C₄ and Q=C₃⋊S₄

Direct product G=N×Q with N=C₄ and Q=C₃⋊S₄

		d	ρ	Label	ID
C₄×C₃⋊S₄		36	6	C4xC3:S4	288,908

Semidirect products G=N:Q with N=C₄ and Q=C₃⋊S₄

extension	φ:Q→Aut N	d	ρ	Label	ID
C₄⋊(C₃⋊S₄) = C₁₂⋊S₄	φ: C₃⋊S₄/C₃×A₄ → C₂ ⊆ Aut C₄	36	6+	C4:(C3:S4)	288,909

Non-split extensions G=N.Q with N=C₄ and Q=C₃⋊S₄

extension	φ:Q→Aut N	d	ρ	Label	ID
C₄.₁(C₃⋊S₄) = A₄⋊Dic₆	φ: C₃⋊S₄/C₃×A₄ → C₂ ⊆ Aut C₄	72	6-	C4.1(C3:S4)	288,907
C₄.₂(C₃⋊S₄) = C₁₂.₆S₄	φ: C₃⋊S₄/C₃×A₄ → C₂ ⊆ Aut C₄	96	4-	C4.2(C3:S4)	288,913
C₄.₃(C₃⋊S₄) = C₁₂.₇S₄	φ: C₃⋊S₄/C₃×A₄ → C₂ ⊆ Aut C₄	48	4+	C4.3(C3:S4)	288,915
C₄.₄(C₃⋊S₄) = C₁₂.₁₂S₄	central extension (φ=1)	72	6	C4.4(C3:S4)	288,402
C₄.₅(C₃⋊S₄) = C₃⋊U₂(𝔽₃)	central extension (φ=1)	72	4	C4.5(C3:S4)	288,404
C₄.₆(C₃⋊S₄) = C₁₂.₁₄S₄	central extension (φ=1)	48	4	C4.6(C3:S4)	288,914

׿

×

⋊

ℤ

𝔽

○

≀

ℚ

◁