Extensions 1→N→G→Q→1 with N=C₂²×He₃ and Q=C₄

Direct product G=N×Q with N=C₂²×He₃ and Q=C₄

		d	ρ	Label	ID
C₂²×C₄×He₃		144		C2^2xC4xHe3	432,401

Semidirect products G=N:Q with N=C₂²×He₃ and Q=C₄

extension	φ:Q→Out N	d	ρ	Label	ID
(C₂²×He₃)⋊₁C₄ = C₂²⋊(He₃⋊C₄)	φ: C₄/C₁ → C₄ ⊆ Out C₂²×He₃	36	6	(C2^2xHe3):1C4	432,279
(C₂²×He₃)⋊₂C₄ = C₂²×He₃⋊C₄	φ: C₄/C₁ → C₄ ⊆ Out C₂²×He₃	72		(C2^2xHe3):2C4	432,543
(C₂²×He₃)⋊₃C₄ = C₂²⋊C₄×He₃	φ: C₄/C₂ → C₂ ⊆ Out C₂²×He₃	72		(C2^2xHe3):3C4	432,204
(C₂²×He₃)⋊₄C₄ = C₆²⋊₃C₁₂	φ: C₄/C₂ → C₂ ⊆ Out C₂²×He₃	72		(C2^2xHe3):4C4	432,166
(C₂²×He₃)⋊₅C₄ = C₆²⋊₄Dic₃	φ: C₄/C₂ → C₂ ⊆ Out C₂²×He₃	72		(C2^2xHe3):5C4	432,199
(C₂²×He₃)⋊₆C₄ = C₂²×C₃²⋊C₁₂	φ: C₄/C₂ → C₂ ⊆ Out C₂²×He₃	144		(C2^2xHe3):6C4	432,376
(C₂²×He₃)⋊₇C₄ = C₂²×He₃⋊₃C₄	φ: C₄/C₂ → C₂ ⊆ Out C₂²×He₃	144		(C2^2xHe3):7C4	432,398

Non-split extensions G=N.Q with N=C₂²×He₃ and Q=C₄

extension	φ:Q→Out N	d	ρ	Label	ID
(C₂²×He₃).₁C₄ = C₂×He₃⋊₂C₈	φ: C₄/C₁ → C₄ ⊆ Out C₂²×He₃	144		(C2^2xHe3).1C4	432,277
(C₂²×He₃).₂C₄ = He₃⋊₄M₄(2)	φ: C₄/C₁ → C₄ ⊆ Out C₂²×He₃	72	6	(C2^2xHe3).2C4	432,278
(C₂²×He₃).₃C₄ = M₄(2)×He₃	φ: C₄/C₂ → C₂ ⊆ Out C₂²×He₃	72	6	(C2^2xHe3).3C4	432,213
(C₂²×He₃).₄C₄ = C₂×He₃⋊₃C₈	φ: C₄/C₂ → C₂ ⊆ Out C₂²×He₃	144		(C2^2xHe3).4C4	432,136
(C₂²×He₃).₅C₄ = He₃⋊₇M₄(2)	φ: C₄/C₂ → C₂ ⊆ Out C₂²×He₃	72	6	(C2^2xHe3).5C4	432,137
(C₂²×He₃).₆C₄ = C₂×He₃⋊₄C₈	φ: C₄/C₂ → C₂ ⊆ Out C₂²×He₃	144		(C2^2xHe3).6C4	432,184
(C₂²×He₃).₇C₄ = He₃⋊₈M₄(2)	φ: C₄/C₂ → C₂ ⊆ Out C₂²×He₃	72	6	(C2^2xHe3).7C4	432,185
(C₂²×He₃).₈C₄ = C₂×C₈×He₃	φ: trivial image	144		(C2^2xHe3).8C4	432,210

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