Extensions 1→N→G→Q→1 with N=C₃ and Q=M₄(2)⋊S₃

Direct product G=N×Q with N=C₃ and Q=M₄(2)⋊S₃

		d	ρ	Label	ID
C₃×M₄(2)⋊S₃		48	4	C3xM4(2):S3	288,257

Semidirect products G=N:Q with N=C₃ and Q=M₄(2)⋊S₃

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃⋊₁(M₄(2)⋊S₃) = C₁₂.₇₀D₁₂	φ: M₄(2)⋊S₃/C₄.Dic₃ → C₂ ⊆ Aut C₃	24	4+	C3:1(M4(2):S3)	288,207
C₃⋊₂(M₄(2)⋊S₃) = C₁₂.₁₉D₁₂	φ: M₄(2)⋊S₃/C₃×M₄(2) → C₂ ⊆ Aut C₃	72		C3:2(M4(2):S3)	288,298
C₃⋊₃(M₄(2)⋊S₃) = C₁₂.D₁₂	φ: M₄(2)⋊S₃/C₂×D₁₂ → C₂ ⊆ Aut C₃	48	4	C3:3(M4(2):S3)	288,206

Non-split extensions G=N.Q with N=C₃ and Q=M₄(2)⋊S₃

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃.(M₄(2)⋊S₃) = M₄(2)⋊D₉	φ: M₄(2)⋊S₃/C₃×M₄(2) → C₂ ⊆ Aut C₃	72	4+	C3.(M4(2):S3)	288,31

⋊

ℤ

𝔽

○

≀

ℚ

◁

Extensions 1→N→G→Q→1 with N=C3 and Q=M4(2)⋊S3