Extensions 1→N→G→Q→1 with N=C₂²×He₃⋊C₂ and Q=C₂

Direct product G=N×Q with N=C₂²×He₃⋊C₂ and Q=C₂

		d	ρ	Label	ID
C₂³×He₃⋊C₂		72		C2^3xHe3:C2	432,561

Semidirect products G=N:Q with N=C₂²×He₃⋊C₂ and Q=C₂

extension	φ:Q→Out N	d	ρ	Label	ID
(C₂²×He₃⋊C₂)⋊₁C₂ = C₂×He₃⋊₃D₄	φ: C₂/C₁ → C₂ ⊆ Out C₂²×He₃⋊C₂	72		(C2^2xHe3:C2):1C2	432,322
(C₂²×He₃⋊C₂)⋊₂C₂ = C₆²⋊₂D₆	φ: C₂/C₁ → C₂ ⊆ Out C₂²×He₃⋊C₂	36	6	(C2^2xHe3:C2):2C2	432,324
(C₂²×He₃⋊C₂)⋊₃C₂ = C₂×He₃⋊₅D₄	φ: C₂/C₁ → C₂ ⊆ Out C₂²×He₃⋊C₂	72		(C2^2xHe3:C2):3C2	432,386
(C₂²×He₃⋊C₂)⋊₄C₂ = D₄×He₃⋊C₂	φ: C₂/C₁ → C₂ ⊆ Out C₂²×He₃⋊C₂	36	6	(C2^2xHe3:C2):4C2	432,390
(C₂²×He₃⋊C₂)⋊₅C₂ = C₂×He₃⋊₇D₄	φ: C₂/C₁ → C₂ ⊆ Out C₂²×He₃⋊C₂	72		(C2^2xHe3:C2):5C2	432,399
(C₂²×He₃⋊C₂)⋊₆C₂ = C₂²×C₃²⋊D₆	φ: C₂/C₁ → C₂ ⊆ Out C₂²×He₃⋊C₂	36		(C2^2xHe3:C2):6C2	432,545

Non-split extensions G=N.Q with N=C₂²×He₃⋊C₂ and Q=C₂

extension	φ:Q→Out N	d	ρ	Label	ID
(C₂²×He₃⋊C₂).₁C₂ = C₆².₅D₆	φ: C₂/C₁ → C₂ ⊆ Out C₂²×He₃⋊C₂	72		(C2^2xHe3:C2).1C2	432,98
(C₂²×He₃⋊C₂).₂C₂ = C₆².₃₁D₆	φ: C₂/C₁ → C₂ ⊆ Out C₂²×He₃⋊C₂	72		(C2^2xHe3:C2).2C2	432,189
(C₂²×He₃⋊C₂).₃C₂ = C₂²⋊(He₃⋊C₄)	φ: C₂/C₁ → C₂ ⊆ Out C₂²×He₃⋊C₂	36	6	(C2^2xHe3:C2).3C2	432,279
(C₂²×He₃⋊C₂).₄C₂ = C₂×He₃⋊(C₂×C₄)	φ: C₂/C₁ → C₂ ⊆ Out C₂²×He₃⋊C₂	72		(C2^2xHe3:C2).4C2	432,321
(C₂²×He₃⋊C₂).₅C₂ = C₂²×He₃⋊C₄	φ: C₂/C₁ → C₂ ⊆ Out C₂²×He₃⋊C₂	72		(C2^2xHe3:C2).5C2	432,543
(C₂²×He₃⋊C₂).₆C₂ = C₂×C₄×He₃⋊C₂	φ: trivial image	72		(C2^2xHe3:C2).6C2	432,385

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