Extensions 1→N→G→Q→1 with N=He₃⋊₃C₄ and Q=C₄

Direct product G=N×Q with N=He₃⋊₃C₄ and Q=C₄

		d	ρ	Label	ID
C₄×He₃⋊₃C₄		144		C4xHe3:3C4	432,186

Semidirect products G=N:Q with N=He₃⋊₃C₄ and Q=C₄

extension	φ:Q→Out N	d	ρ	Label	ID
He₃⋊₃C₄⋊₁C₄ = C₄×He₃⋊C₄	φ: C₄/C₂ → C₂ ⊆ Out He₃⋊₃C₄	72	3	He3:3C4:1C4	432,275
He₃⋊₃C₄⋊₂C₄ = C₆².₃D₆	φ: C₄/C₂ → C₂ ⊆ Out He₃⋊₃C₄	144		He3:3C4:2C4	432,96
He₃⋊₃C₄⋊₃C₄ = He₃⋊C₄²	φ: C₄/C₂ → C₂ ⊆ Out He₃⋊₃C₄	144		He3:3C4:3C4	432,94
He₃⋊₃C₄⋊₄C₄ = C₆².₂₉D₆	φ: C₄/C₂ → C₂ ⊆ Out He₃⋊₃C₄	144		He3:3C4:4C4	432,187
He₃⋊₃C₄⋊₅C₄ = C₄⋊(He₃⋊C₄)	φ: C₄/C₂ → C₂ ⊆ Out He₃⋊₃C₄	72	6	He3:3C4:5C4	432,276

Non-split extensions G=N.Q with N=He₃⋊₃C₄ and Q=C₄

extension	φ:Q→Out N	d	ρ	Label	ID
He₃⋊₃C₄.C₄ = He₃⋊C₁₆	φ: C₄/C₁ → C₄ ⊆ Out He₃⋊₃C₄	144	6	He3:3C4.C4	432,233
He₃⋊₃C₄.₂C₄ = C₂×He₃⋊₂C₈	φ: C₄/C₂ → C₂ ⊆ Out He₃⋊₃C₄	144		He3:3C4.2C4	432,277
He₃⋊₃C₄.₃C₄ = He₃⋊₃M₄(2)	φ: C₄/C₂ → C₂ ⊆ Out He₃⋊₃C₄	72	6	He3:3C4.3C4	432,82
He₃⋊₃C₄.₄C₄ = C₁₂.₈₉S₃²	φ: C₄/C₂ → C₂ ⊆ Out He₃⋊₃C₄	72	6	He3:3C4.4C4	432,81
He₃⋊₃C₄.₅C₄ = He₃⋊₆M₄(2)	φ: C₄/C₂ → C₂ ⊆ Out He₃⋊₃C₄	72	6	He3:3C4.5C4	432,174
He₃⋊₃C₄.₆C₄ = He₃⋊₄M₄(2)	φ: C₄/C₂ → C₂ ⊆ Out He₃⋊₃C₄	72	6	He3:3C4.6C4	432,278
He₃⋊₃C₄.₇C₄ = C₈×He₃⋊C₂	φ: trivial image	72	3	He3:3C4.7C4	432,173

׿

×

⋊

ℤ

𝔽

○

≀

ℚ

◁