Extensions 1→N→G→Q→1 with N=C₃ and Q=C₃×D₄⋊₂S₃

Direct product G=N×Q with N=C₃ and Q=C₃×D₄⋊₂S₃

		d	ρ	Label	ID
C₃²×D₄⋊₂S₃		72		C3^2xD4:2S3	432,705

Semidirect products G=N:Q with N=C₃ and Q=C₃×D₄⋊₂S₃

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃⋊₁(C₃×D₄⋊₂S₃) = C₃×D₁₂⋊S₃	φ: C₃×D₄⋊₂S₃/C₃×Dic₆ → C₂ ⊆ Aut C₃	48	4	C3:1(C3xD4:2S3)	432,644
C₃⋊₂(C₃×D₄⋊₂S₃) = C₃×D₁₂⋊₅S₃	φ: C₃×D₄⋊₂S₃/S₃×C₁₂ → C₂ ⊆ Aut C₃	48	4	C3:2(C3xD4:2S3)	432,643
C₃⋊₃(C₃×D₄⋊₂S₃) = C₃×D₆.₃D₆	φ: C₃×D₄⋊₂S₃/C₆×Dic₃ → C₂ ⊆ Aut C₃	24	4	C3:3(C3xD4:2S3)	432,652
C₃⋊₄(C₃×D₄⋊₂S₃) = C₃×D₆.₄D₆	φ: C₃×D₄⋊₂S₃/C₃×C₃⋊D₄ → C₂ ⊆ Aut C₃	24	4	C3:4(C3xD4:2S3)	432,653
C₃⋊₅(C₃×D₄⋊₂S₃) = C₃×C₁₂.D₆	φ: C₃×D₄⋊₂S₃/D₄×C₃² → C₂ ⊆ Aut C₃	72		C3:5(C3xD4:2S3)	432,715

Non-split extensions G=N.Q with N=C₃ and Q=C₃×D₄⋊₂S₃

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃.₁(C₃×D₄⋊₂S₃) = C₃×D₄⋊₂D₉	φ: C₃×D₄⋊₂S₃/D₄×C₃² → C₂ ⊆ Aut C₃	72	4	C3.1(C3xD4:2S3)	432,357
C₃.₂(C₃×D₄⋊₂S₃) = C₆².₁₃D₆	φ: C₃×D₄⋊₂S₃/D₄×C₃² → C₂ ⊆ Aut C₃	72	12-	C3.2(C3xD4:2S3)	432,361
C₃.₃(C₃×D₄⋊₂S₃) = Dic₁₈⋊₂C₆	φ: C₃×D₄⋊₂S₃/D₄×C₃² → C₂ ⊆ Aut C₃	72	12-	C3.3(C3xD4:2S3)	432,363
C₃.₄(C₃×D₄⋊₂S₃) = C₉×D₄⋊₂S₃	central extension (φ=1)	72	4	C3.4(C3xD4:2S3)	432,359

׿

×

⋊

ℤ

𝔽

○

≀

ℚ

◁