Extensions 1→N→G→Q→1 with N=D₄ and Q=C₂×Dic₃

Direct product G=N×Q with N=D₄ and Q=C₂×Dic₃

		d	ρ	Label	ID
C₂×D₄×Dic₃		96		C2xD4xDic3	192,1354

Semidirect products G=N:Q with N=D₄ and Q=C₂×Dic₃

extension	φ:Q→Out N	d	ρ	Label	ID
D₄⋊₁(C₂×Dic₃) = Dic₃×D₈	φ: C₂×Dic₃/Dic₃ → C₂ ⊆ Out D₄	96		D4:1(C2xDic3)	192,708
D₄⋊₂(C₂×Dic₃) = D₈⋊Dic₃	φ: C₂×Dic₃/Dic₃ → C₂ ⊆ Out D₄	96		D4:2(C2xDic3)	192,711
D₄⋊₃(C₂×Dic₃) = C₂×D₄⋊Dic₃	φ: C₂×Dic₃/C₂×C₆ → C₂ ⊆ Out D₄	96		D4:3(C2xDic3)	192,773
D₄⋊₄(C₂×Dic₃) = C₄○D₄⋊₃Dic₃	φ: C₂×Dic₃/C₂×C₆ → C₂ ⊆ Out D₄	96		D4:4(C2xDic3)	192,791
D₄⋊₅(C₂×Dic₃) = C₂×Q₈⋊₃Dic₃	φ: C₂×Dic₃/C₂×C₆ → C₂ ⊆ Out D₄	48		D4:5(C2xDic3)	192,794
D₄⋊₆(C₂×Dic₃) = C₂⁴.₄₉D₆	φ: trivial image	48		D4:6(C2xDic3)	192,1357
D₄⋊₇(C₂×Dic₃) = Dic₃×C₄○D₄	φ: trivial image	96		D4:7(C2xDic3)	192,1385
D₄⋊₈(C₂×Dic₃) = C₆.₁₄₄2₊¹⁺⁴	φ: trivial image	96		D4:8(C2xDic3)	192,1386

Non-split extensions G=N.Q with N=D₄ and Q=C₂×Dic₃

extension	φ:Q→Out N	d	ρ	Label	ID
D₄.₁(C₂×Dic₃) = Dic₃×SD₁₆	φ: C₂×Dic₃/Dic₃ → C₂ ⊆ Out D₄	96		D4.1(C2xDic3)	192,720
D₄.₂(C₂×Dic₃) = SD₁₆⋊Dic₃	φ: C₂×Dic₃/Dic₃ → C₂ ⊆ Out D₄	96		D4.2(C2xDic3)	192,723
D₄.₃(C₂×Dic₃) = D₈⋊₅Dic₃	φ: C₂×Dic₃/Dic₃ → C₂ ⊆ Out D₄	48	4	D4.3(C2xDic3)	192,755
D₄.₄(C₂×Dic₃) = D₈⋊₄Dic₃	φ: C₂×Dic₃/Dic₃ → C₂ ⊆ Out D₄	48	4	D4.4(C2xDic3)	192,756
D₄.₅(C₂×Dic₃) = (C₆×D₄)⋊₆C₄	φ: C₂×Dic₃/C₂×C₆ → C₂ ⊆ Out D₄	48		D4.5(C2xDic3)	192,774
D₄.₆(C₂×Dic₃) = C₄○D₄⋊₄Dic₃	φ: C₂×Dic₃/C₂×C₆ → C₂ ⊆ Out D₄	96		D4.6(C2xDic3)	192,792
D₄.₇(C₂×Dic₃) = (C₆×D₄)⋊₉C₄	φ: C₂×Dic₃/C₂×C₆ → C₂ ⊆ Out D₄	48	4	D4.7(C2xDic3)	192,795
D₄.₈(C₂×Dic₃) = C₂×D₄.Dic₃	φ: trivial image	96		D4.8(C2xDic3)	192,1377
D₄.₉(C₂×Dic₃) = C₁₂.₇₆C₂⁴	φ: trivial image	48	4	D4.9(C2xDic3)	192,1378

׿

×

⋊

ℤ

𝔽

○

≀

ℚ

◁