Extensions 1→N→G→Q→1 with N=C₃ and Q=C₂²×C₃²⋊C₄

Direct product G=N×Q with N=C₃ and Q=C₂²×C₃²⋊C₄

		d	ρ	Label	ID
C₂×C₆×C₃²⋊C₄		48		C2xC6xC3^2:C4	432,765

Semidirect products G=N:Q with N=C₃ and Q=C₂²×C₃²⋊C₄

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃⋊₁(C₂²×C₃²⋊C₄) = C₂×S₃×C₃²⋊C₄	φ: C₂²×C₃²⋊C₄/C₂×C₃²⋊C₄ → C₂ ⊆ Aut C₃	24	8+	C3:1(C2^2xC3^2:C4)	432,753
C₃⋊₂(C₂²×C₃²⋊C₄) = C₂²×C₃³⋊C₄	φ: C₂²×C₃²⋊C₄/C₂²×C₃⋊S₃ → C₂ ⊆ Aut C₃	48		C3:2(C2^2xC3^2:C4)	432,766

Non-split extensions G=N.Q with N=C₃ and Q=C₂²×C₃²⋊C₄

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃.(C₂²×C₃²⋊C₄) = C₂²×He₃⋊C₄	central stem extension (φ=1)	72		C3.(C2^2xC3^2:C4)	432,543

⋊

ℤ

𝔽

○

≀

ℚ

◁

Extensions 1→N→G→Q→1 with N=C3 and Q=C22×C32⋊C4