Extensions 1→N→G→Q→1 with N=C₃ and Q=D₄×C₃²

Direct product G=N×Q with N=C₃ and Q=D₄×C₃²

		d	ρ	Label	ID
D₄×C₃³		108		D4xC3^3	216,151

Semidirect products G=N:Q with N=C₃ and Q=D₄×C₃²

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃⋊₁(D₄×C₃²) = C₃²×D₁₂	φ: D₄×C₃²/C₃×C₁₂ → C₂ ⊆ Aut C₃	72		C3:1(D4xC3^2)	216,137
C₃⋊₂(D₄×C₃²) = C₃²×C₃⋊D₄	φ: D₄×C₃²/C₆² → C₂ ⊆ Aut C₃	36		C3:2(D4xC3^2)	216,139

Non-split extensions G=N.Q with N=C₃ and Q=D₄×C₃²

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃.₁(D₄×C₃²) = D₄×C₃×C₉	central extension (φ=1)	108		C3.1(D4xC3^2)	216,76
C₃.₂(D₄×C₃²) = D₄×He₃	central stem extension (φ=1)	36	6	C3.2(D4xC3^2)	216,77
C₃.₃(D₄×C₃²) = D₄×3_-¹⁺²	central stem extension (φ=1)	36	6	C3.3(D4xC3^2)	216,78

⋊

ℤ

𝔽

○

≀

ℚ

◁

Extensions 1→N→G→Q→1 with N=C3 and Q=D4×C32