Extensions 1→N→G→Q→1 with N=D₄ and Q=C₂×C₁₈

Direct product G=N×Q with N=D₄ and Q=C₂×C₁₈

		d	ρ	Label	ID
D₄×C₂×C₁₈		144		D4xC2xC18	288,368

Semidirect products G=N:Q with N=D₄ and Q=C₂×C₁₈

extension	φ:Q→Out N	d	ρ	Label	ID
D₄⋊₁(C₂×C₁₈) = D₈×C₁₈	φ: C₂×C₁₈/C₁₈ → C₂ ⊆ Out D₄	144		D4:1(C2xC18)	288,182
D₄⋊₂(C₂×C₁₈) = C₉×C₈⋊C₂²	φ: C₂×C₁₈/C₁₈ → C₂ ⊆ Out D₄	72	4	D4:2(C2xC18)	288,186
D₄⋊₃(C₂×C₁₈) = C₄○D₄×C₁₈	φ: trivial image	144		D4:3(C2xC18)	288,370
D₄⋊₄(C₂×C₁₈) = C₉×2₊¹⁺⁴	φ: trivial image	72	4	D4:4(C2xC18)	288,371

Non-split extensions G=N.Q with N=D₄ and Q=C₂×C₁₈

extension	φ:Q→Out N	d	ρ	Label	ID
D₄.₁(C₂×C₁₈) = SD₁₆×C₁₈	φ: C₂×C₁₈/C₁₈ → C₂ ⊆ Out D₄	144		D4.1(C2xC18)	288,183
D₄.₂(C₂×C₁₈) = C₉×C₄○D₈	φ: C₂×C₁₈/C₁₈ → C₂ ⊆ Out D₄	144	2	D4.2(C2xC18)	288,185
D₄.₃(C₂×C₁₈) = C₉×C₈.C₂²	φ: C₂×C₁₈/C₁₈ → C₂ ⊆ Out D₄	144	4	D4.3(C2xC18)	288,187
D₄.₄(C₂×C₁₈) = C₉×2_-¹⁺⁴	φ: trivial image	144	4	D4.4(C2xC18)	288,372

׿

×

⋊

ℤ

𝔽

○

≀

ℚ

◁