Extensions 1→N→G→Q→1 with N=C₃⁴ and Q=C₄

Direct product G=N×Q with N=C₃⁴ and Q=C₄

		d	ρ	Label	ID
C₃³×C₁₂		324		C3^3xC12	324,159

Semidirect products G=N:Q with N=C₃⁴ and Q=C₄

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃⁴⋊₁C₄ = C₃²×C₃²⋊C₄	φ: C₄/C₁ → C₄ ⊆ Aut C₃⁴	36		C3^4:1C4	324,161
C₃⁴⋊₂C₄ = C₃×C₃³⋊C₄	φ: C₄/C₁ → C₄ ⊆ Aut C₃⁴	12	4	C3^4:2C4	324,162
C₃⁴⋊₃C₄ = C₃⁴⋊C₄	φ: C₄/C₁ → C₄ ⊆ Aut C₃⁴	36		C3^4:3C4	324,163
C₃⁴⋊₄C₄ = C₃⁴⋊₄C₄	φ: C₄/C₁ → C₄ ⊆ Aut C₃⁴	18		C3^4:4C4	324,164
C₃⁴⋊₅C₄ = Dic₃×C₃³	φ: C₄/C₂ → C₂ ⊆ Aut C₃⁴	108		C3^4:5C4	324,155
C₃⁴⋊₆C₄ = C₃²×C₃⋊Dic₃	φ: C₄/C₂ → C₂ ⊆ Aut C₃⁴	36		C3^4:6C4	324,156
C₃⁴⋊₇C₄ = C₃×C₃³⋊₅C₄	φ: C₄/C₂ → C₂ ⊆ Aut C₃⁴	108		C3^4:7C4	324,157
C₃⁴⋊₈C₄ = C₃⁴⋊₈C₄	φ: C₄/C₂ → C₂ ⊆ Aut C₃⁴	324		C3^4:8C4	324,158

׿

×

⋊

ℤ

𝔽

○

≀

ℚ

◁