Extensions 1→N→G→Q→1 with N=M₄(2) and Q=Dic₃

Direct product G=N×Q with N=M₄(2) and Q=Dic₃

		d	ρ	Label	ID
Dic₃×M₄(2)		96		Dic3xM4(2)	192,676

Semidirect products G=N:Q with N=M₄(2) and Q=Dic₃

extension	φ:Q→Out N	d	ρ	Label	ID
M₄(2)⋊₁Dic₃ = C₂³.₅₂D₁₂	φ: Dic₃/C₆ → C₂ ⊆ Out M₄(2)	96		M4(2):1Dic3	192,680
M₄(2)⋊₂Dic₃ = M₄(2)⋊Dic₃	φ: Dic₃/C₆ → C₂ ⊆ Out M₄(2)	96		M4(2):2Dic3	192,113
M₄(2)⋊₃Dic₃ = C₁₂.₃C₄²	φ: Dic₃/C₆ → C₂ ⊆ Out M₄(2)	48		M4(2):3Dic3	192,114
M₄(2)⋊₄Dic₃ = M₄(2)⋊₄Dic₃	φ: Dic₃/C₆ → C₂ ⊆ Out M₄(2)	48	4	M4(2):4Dic3	192,118
M₄(2)⋊₅Dic₃ = C₁₂.₇C₄²	φ: trivial image	96		M4(2):5Dic3	192,681

Non-split extensions G=N.Q with N=M₄(2) and Q=Dic₃

extension	φ:Q→Out N	d	ρ	Label	ID
M₄(2).₁Dic₃ = C₂³.₉Dic₆	φ: Dic₃/C₆ → C₂ ⊆ Out M₄(2)	48	4	M4(2).1Dic3	192,684
M₄(2).₂Dic₃ = C₁₂.₄C₄²	φ: Dic₃/C₆ → C₂ ⊆ Out M₄(2)	96		M4(2).2Dic3	192,117
M₄(2).₃Dic₃ = C₂₄.₉₉D₄	φ: Dic₃/C₆ → C₂ ⊆ Out M₄(2)	96	4	M4(2).3Dic3	192,120
M₄(2).₄Dic₃ = C₂₄.₇₈C₂³	φ: trivial image	96	4	M4(2).4Dic3	192,699

׿

×

⋊

ℤ

𝔽

○

≀

ℚ

◁