Extensions 1→N→G→Q→1 with N=C₂³×He₃ and Q=C₂

Direct product G=N×Q with N=C₂³×He₃ and Q=C₂

		d	ρ	Label	ID
C₂⁴×He₃		144		C2^4xHe3	432,563

Semidirect products G=N:Q with N=C₂³×He₃ and Q=C₂

extension	φ:Q→Out N	d	ρ	Label	ID
(C₂³×He₃)⋊₁C₂ = C₂×D₄×He₃	φ: C₂/C₁ → C₂ ⊆ Out C₂³×He₃	72		(C2^3xHe3):1C2	432,404
(C₂³×He₃)⋊₂C₂ = C₂×He₃⋊₆D₄	φ: C₂/C₁ → C₂ ⊆ Out C₂³×He₃	72		(C2^3xHe3):2C2	432,377
(C₂³×He₃)⋊₃C₂ = C₂×He₃⋊₇D₄	φ: C₂/C₁ → C₂ ⊆ Out C₂³×He₃	72		(C2^3xHe3):3C2	432,399
(C₂³×He₃)⋊₄C₂ = C₂³×C₃²⋊C₆	φ: C₂/C₁ → C₂ ⊆ Out C₂³×He₃	72		(C2^3xHe3):4C2	432,558
(C₂³×He₃)⋊₅C₂ = C₂³×He₃⋊C₂	φ: C₂/C₁ → C₂ ⊆ Out C₂³×He₃	72		(C2^3xHe3):5C2	432,561

Non-split extensions G=N.Q with N=C₂³×He₃ and Q=C₂

extension	φ:Q→Out N	d	ρ	Label	ID
(C₂³×He₃).₁C₂ = C₂²⋊C₄×He₃	φ: C₂/C₁ → C₂ ⊆ Out C₂³×He₃	72		(C2^3xHe3).1C2	432,204
(C₂³×He₃).₂C₂ = C₆²⋊₃C₁₂	φ: C₂/C₁ → C₂ ⊆ Out C₂³×He₃	72		(C2^3xHe3).2C2	432,166
(C₂³×He₃).₃C₂ = C₆²⋊₄Dic₃	φ: C₂/C₁ → C₂ ⊆ Out C₂³×He₃	72		(C2^3xHe3).3C2	432,199
(C₂³×He₃).₄C₂ = C₂²×C₃²⋊C₁₂	φ: C₂/C₁ → C₂ ⊆ Out C₂³×He₃	144		(C2^3xHe3).4C2	432,376
(C₂³×He₃).₅C₂ = C₂²×He₃⋊₃C₄	φ: C₂/C₁ → C₂ ⊆ Out C₂³×He₃	144		(C2^3xHe3).5C2	432,398
(C₂³×He₃).₆C₂ = C₂²×C₄×He₃	φ: trivial image	144		(C2^3xHe3).6C2	432,401

׿

×

⋊

ℤ

𝔽

○

≀

ℚ

◁