Extensions 1→N→G→Q→1 with N=C₃ and Q=D₄⋊S₃

Direct product G=N×Q with N=C₃ and Q=D₄⋊S₃

		d	ρ	Label	ID
C₃×D₄⋊S₃		24	4	C3xD4:S3	144,80

Semidirect products G=N:Q with N=C₃ and Q=D₄⋊S₃

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃⋊₁(D₄⋊S₃) = C₃⋊D₂₄	φ: D₄⋊S₃/C₃⋊C₈ → C₂ ⊆ Aut C₃	24	4+	C3:1(D4:S3)	144,57
C₃⋊₂(D₄⋊S₃) = C₃²⋊₂D₈	φ: D₄⋊S₃/D₁₂ → C₂ ⊆ Aut C₃	48	4	C3:2(D4:S3)	144,56
C₃⋊₃(D₄⋊S₃) = C₃²⋊₇D₈	φ: D₄⋊S₃/C₃×D₄ → C₂ ⊆ Aut C₃	72		C3:3(D4:S3)	144,96

Non-split extensions G=N.Q with N=C₃ and Q=D₄⋊S₃

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃.(D₄⋊S₃) = D₄⋊D₉	φ: D₄⋊S₃/C₃×D₄ → C₂ ⊆ Aut C₃	72	4+	C3.(D4:S3)	144,16

⋊

ℤ

𝔽

○

≀

ℚ

◁

Extensions 1→N→G→Q→1 with N=C3 and Q=D4⋊S3