Extensions 1→N→G→Q→1 with N=C₃×C₂₁ and Q=S₃

Direct product G=N×Q with N=C₃×C₂₁ and Q=S₃

		d	ρ	Label	ID
S₃×C₃×C₂₁		126		S3xC3xC21	378,54

Semidirect products G=N:Q with N=C₃×C₂₁ and Q=S₃

extension	φ:Q→Aut N	d	ρ	Label	ID
(C₃×C₂₁)⋊₁S₃ = He₃⋊D₇	φ: S₃/C₁ → S₃ ⊆ Aut C₃×C₂₁	63	6+	(C3xC21):1S3	378,38
(C₃×C₂₁)⋊₂S₃ = C₃²⋊D₂₁	φ: S₃/C₁ → S₃ ⊆ Aut C₃×C₂₁	63	6	(C3xC21):2S3	378,43
(C₃×C₂₁)⋊₃S₃ = C₇×C₃²⋊C₆	φ: S₃/C₁ → S₃ ⊆ Aut C₃×C₂₁	63	6	(C3xC21):3S3	378,34
(C₃×C₂₁)⋊₄S₃ = C₇×He₃⋊C₂	φ: S₃/C₁ → S₃ ⊆ Aut C₃×C₂₁	63	3	(C3xC21):4S3	378,41
(C₃×C₂₁)⋊₅S₃ = C₃³⋊D₇	φ: S₃/C₃ → C₂ ⊆ Aut C₃×C₂₁	189		(C3xC21):5S3	378,59
(C₃×C₂₁)⋊₆S₃ = C₃×C₃⋊D₂₁	φ: S₃/C₃ → C₂ ⊆ Aut C₃×C₂₁	126		(C3xC21):6S3	378,57
(C₃×C₂₁)⋊₇S₃ = C₃²×D₂₁	φ: S₃/C₃ → C₂ ⊆ Aut C₃×C₂₁	126		(C3xC21):7S3	378,55
(C₃×C₂₁)⋊₈S₃ = C₃⋊S₃×C₂₁	φ: S₃/C₃ → C₂ ⊆ Aut C₃×C₂₁	126		(C3xC21):8S3	378,56
(C₃×C₂₁)⋊₉S₃ = C₇×C₃³⋊C₂	φ: S₃/C₃ → C₂ ⊆ Aut C₃×C₂₁	189		(C3xC21):9S3	378,58

Non-split extensions G=N.Q with N=C₃×C₂₁ and Q=S₃

extension	φ:Q→Aut N	d	ρ	Label	ID
(C₃×C₂₁).₁S₃ = D₆₃⋊C₃	φ: S₃/C₁ → S₃ ⊆ Aut C₃×C₂₁	63	6+	(C3xC21).1S3	378,39
(C₃×C₂₁).₂S₃ = C₇×C₉⋊C₆	φ: S₃/C₁ → S₃ ⊆ Aut C₃×C₂₁	63	6	(C3xC21).2S3	378,35
(C₃×C₂₁).₃S₃ = C₃⋊D₆₃	φ: S₃/C₃ → C₂ ⊆ Aut C₃×C₂₁	189		(C3xC21).3S3	378,42
(C₃×C₂₁).₄S₃ = C₃×D₆₃	φ: S₃/C₃ → C₂ ⊆ Aut C₃×C₂₁	126	2	(C3xC21).4S3	378,36
(C₃×C₂₁).₅S₃ = D₉×C₂₁	φ: S₃/C₃ → C₂ ⊆ Aut C₃×C₂₁	126	2	(C3xC21).5S3	378,32
(C₃×C₂₁).₆S₃ = C₇×C₉⋊S₃	φ: S₃/C₃ → C₂ ⊆ Aut C₃×C₂₁	189		(C3xC21).6S3	378,40

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