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

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

		d	ρ	Label	ID
C₄²×He₃		144		C4^2xHe3	432,201

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

extension	φ:Q→Out N	d	ρ	Label	ID
(C₄×He₃)⋊₁C₄ = C₄×He₃⋊C₄	φ: C₄/C₁ → C₄ ⊆ Out C₄×He₃	72	3	(C4xHe3):1C4	432,275
(C₄×He₃)⋊₂C₄ = C₄⋊(He₃⋊C₄)	φ: C₄/C₁ → C₄ ⊆ Out C₄×He₃	72	6	(C4xHe3):2C4	432,276
(C₄×He₃)⋊₃C₄ = C₆².₂₀D₆	φ: C₄/C₂ → C₂ ⊆ Out C₄×He₃	144		(C4xHe3):3C4	432,140
(C₄×He₃)⋊₄C₄ = C₆².₃₀D₆	φ: C₄/C₂ → C₂ ⊆ Out C₄×He₃	144		(C4xHe3):4C4	432,188
(C₄×He₃)⋊₅C₄ = C₄×C₃²⋊C₁₂	φ: C₄/C₂ → C₂ ⊆ Out C₄×He₃	144		(C4xHe3):5C4	432,138
(C₄×He₃)⋊₆C₄ = C₄×He₃⋊₃C₄	φ: C₄/C₂ → C₂ ⊆ Out C₄×He₃	144		(C4xHe3):6C4	432,186
(C₄×He₃)⋊₇C₄ = C₄⋊C₄×He₃	φ: C₄/C₂ → C₂ ⊆ Out C₄×He₃	144		(C4xHe3):7C4	432,207

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

extension	φ:Q→Out N	d	ρ	Label	ID
(C₄×He₃).₁C₄ = He₃⋊₂C₁₆	φ: C₄/C₁ → C₄ ⊆ Out C₄×He₃	144	3	(C4xHe3).1C4	432,57
(C₄×He₃).₂C₄ = He₃⋊₂(C₂×C₈)	φ: C₄/C₁ → C₄ ⊆ Out C₄×He₃	72	3	(C4xHe3).2C4	432,273
(C₄×He₃).₃C₄ = He₃⋊₁M₄(2)	φ: C₄/C₁ → C₄ ⊆ Out C₄×He₃	72	6	(C4xHe3).3C4	432,274
(C₄×He₃).₄C₄ = He₃⋊₇M₄(2)	φ: C₄/C₂ → C₂ ⊆ Out C₄×He₃	72	6	(C4xHe3).4C4	432,137
(C₄×He₃).₅C₄ = He₃⋊₈M₄(2)	φ: C₄/C₂ → C₂ ⊆ Out C₄×He₃	72	6	(C4xHe3).5C4	432,185
(C₄×He₃).₆C₄ = He₃⋊₃C₁₆	φ: C₄/C₂ → C₂ ⊆ Out C₄×He₃	144	6	(C4xHe3).6C4	432,30
(C₄×He₃).₇C₄ = He₃⋊₄C₁₆	φ: C₄/C₂ → C₂ ⊆ Out C₄×He₃	144	3	(C4xHe3).7C4	432,33
(C₄×He₃).₈C₄ = C₂×He₃⋊₃C₈	φ: C₄/C₂ → C₂ ⊆ Out C₄×He₃	144		(C4xHe3).8C4	432,136
(C₄×He₃).₉C₄ = C₂×He₃⋊₄C₈	φ: C₄/C₂ → C₂ ⊆ Out C₄×He₃	144		(C4xHe3).9C4	432,184
(C₄×He₃).₁₀C₄ = M₄(2)×He₃	φ: C₄/C₂ → C₂ ⊆ Out C₄×He₃	72	6	(C4xHe3).10C4	432,213
(C₄×He₃).₁₁C₄ = C₁₆×He₃	φ: trivial image	144	3	(C4xHe3).11C4	432,35
(C₄×He₃).₁₂C₄ = C₂×C₈×He₃	φ: trivial image	144		(C4xHe3).12C4	432,210

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