Extensions 1→N→G→Q→1 with N=C₃ and Q=C₃×D₄⋊C₄

Direct product G=N×Q with N=C₃ and Q=C₃×D₄⋊C₄

		d	ρ	Label	ID
C₃²×D₄⋊C₄		144		C3^2xD4:C4	288,320

Semidirect products G=N:Q with N=C₃ and Q=C₃×D₄⋊C₄

extension	φ:Q→Aut N	d	Label	ID
C₃⋊₁(C₃×D₄⋊C₄) = C₃×C₆.D₈	φ: C₃×D₄⋊C₄/C₃×C₄⋊C₄ → C₂ ⊆ Aut C₃	96	C3:1(C3xD4:C4)	288,243
C₃⋊₂(C₃×D₄⋊C₄) = C₃×C₂.D₂₄	φ: C₃×D₄⋊C₄/C₂×C₂₄ → C₂ ⊆ Aut C₃	96	C3:2(C3xD4:C4)	288,255
C₃⋊₃(C₃×D₄⋊C₄) = C₃×D₄⋊Dic₃	φ: C₃×D₄⋊C₄/C₆×D₄ → C₂ ⊆ Aut C₃	48	C3:3(C3xD4:C4)	288,266

Non-split extensions G=N.Q with N=C₃ and Q=C₃×D₄⋊C₄

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃.(C₃×D₄⋊C₄) = C₉×D₄⋊C₄	central extension (φ=1)	144		C3.(C3xD4:C4)	288,52

⋊

ℤ

𝔽

○

≀

ℚ

◁

Extensions 1→N→G→Q→1 with N=C3 and Q=C3×D4⋊C4