Extensions 1→N→G→Q→1 with N=C₃×C₇⋊C₃ and Q=C₆

Direct product G=N×Q with N=C₃×C₇⋊C₃ and Q=C₆

		d	ρ	Label	ID
C₃×C₆×C₇⋊C₃		126		C3xC6xC7:C3	378,52

Semidirect products G=N:Q with N=C₃×C₇⋊C₃ and Q=C₆

extension	φ:Q→Out N	d	ρ	Label	ID
(C₃×C₇⋊C₃)⋊C₆ = D₇⋊He₃	φ: C₆/C₁ → C₆ ⊆ Out C₃×C₇⋊C₃	63	6	(C3xC7:C3):C6	378,12
(C₃×C₇⋊C₃)⋊₂C₆ = C₂×C₇⋊He₃	φ: C₆/C₂ → C₃ ⊆ Out C₃×C₇⋊C₃	126	3	(C3xC7:C3):2C6	378,28
(C₃×C₇⋊C₃)⋊₃C₆ = C₃×C₃⋊F₇	φ: C₆/C₃ → C₂ ⊆ Out C₃×C₇⋊C₃	42	6	(C3xC7:C3):3C6	378,49
(C₃×C₇⋊C₃)⋊₄C₆ = C₃²×F₇	φ: C₆/C₃ → C₂ ⊆ Out C₃×C₇⋊C₃	63		(C3xC7:C3):4C6	378,47
(C₃×C₇⋊C₃)⋊₅C₆ = C₃×S₃×C₇⋊C₃	φ: C₆/C₃ → C₂ ⊆ Out C₃×C₇⋊C₃	42	6	(C3xC7:C3):5C6	378,48

Non-split extensions G=N.Q with N=C₃×C₇⋊C₃ and Q=C₆

extension	φ:Q→Out N	d	ρ	Label	ID
(C₃×C₇⋊C₃).₁C₆ = C₉⋊₃F₇	φ: C₆/C₁ → C₆ ⊆ Out C₃×C₇⋊C₃	63	6	(C3xC7:C3).1C6	378,8
(C₃×C₇⋊C₃).₂C₆ = C₉⋊₄F₇	φ: C₆/C₁ → C₆ ⊆ Out C₃×C₇⋊C₃	63	6	(C3xC7:C3).2C6	378,9
(C₃×C₇⋊C₃).₃C₆ = C₂×C₆₃⋊C₃	φ: C₆/C₂ → C₃ ⊆ Out C₃×C₇⋊C₃	126	3	(C3xC7:C3).3C6	378,24
(C₃×C₇⋊C₃).₄C₆ = C₂×C₆₃⋊₃C₃	φ: C₆/C₂ → C₃ ⊆ Out C₃×C₇⋊C₃	126	3	(C3xC7:C3).4C6	378,25
(C₃×C₇⋊C₃).₅C₆ = C₉×F₇	φ: C₆/C₃ → C₂ ⊆ Out C₃×C₇⋊C₃	63	6	(C3xC7:C3).5C6	378,7
(C₃×C₇⋊C₃).₆C₆ = C₁₈×C₇⋊C₃	φ: trivial image	126	3	(C3xC7:C3).6C6	378,23

׿

×

⋊

ℤ

𝔽

○

≀

ℚ

◁