Extensions 1→N→G→Q→1 with N=C₉ and Q=C₃×C₄⋊C₄

Direct product G=N×Q with N=C₉ and Q=C₃×C₄⋊C₄

		d	ρ	Label	ID
C₄⋊C₄×C₃×C₉		432		C4:C4xC3xC9	432,206

Semidirect products G=N:Q with N=C₉ and Q=C₃×C₄⋊C₄

extension	φ:Q→Aut N	d	ρ	Label	ID
C₉⋊₁(C₃×C₄⋊C₄) = Dic₉⋊C₁₂	φ: C₃×C₄⋊C₄/C₂×C₄ → C₆ ⊆ Aut C₉	144		C9:1(C3xC4:C4)	432,145
C₉⋊₂(C₃×C₄⋊C₄) = C₃₆⋊C₁₂	φ: C₃×C₄⋊C₄/C₂×C₄ → C₆ ⊆ Aut C₉	144		C9:2(C3xC4:C4)	432,146
C₉⋊₃(C₃×C₄⋊C₄) = C₄⋊C₄×3_-¹⁺²	φ: C₃×C₄⋊C₄/C₄⋊C₄ → C₃ ⊆ Aut C₉	144		C9:3(C3xC4:C4)	432,208
C₉⋊₄(C₃×C₄⋊C₄) = C₃×Dic₉⋊C₄	φ: C₃×C₄⋊C₄/C₂×C₁₂ → C₂ ⊆ Aut C₉	144		C9:4(C3xC4:C4)	432,129
C₉⋊₅(C₃×C₄⋊C₄) = C₃×C₄⋊Dic₉	φ: C₃×C₄⋊C₄/C₂×C₁₂ → C₂ ⊆ Aut C₉	144		C9:5(C3xC4:C4)	432,130

Non-split extensions G=N.Q with N=C₉ and Q=C₃×C₄⋊C₄

extension	φ:Q→Aut N	d	ρ	Label	ID
C₉.(C₃×C₄⋊C₄) = C₄⋊C₄×C₂₇	central extension (φ=1)	432		C9.(C3xC4:C4)	432,22

׿

×

⋊

ℤ

𝔽

○

≀

ℚ

◁