Extensions 1→N→G→Q→1 with N=C₃×C₆² and Q=C₂

Direct product G=N×Q with N=C₃×C₆² and Q=C₂

		d	ρ	Label	ID
C₆³		216		C6^3	216,177

Semidirect products G=N:Q with N=C₃×C₆² and Q=C₂

extension	φ:Q→Aut N	d	ρ	Label	ID
(C₃×C₆²)⋊₁C₂ = D₄×C₃³	φ: C₂/C₁ → C₂ ⊆ Aut C₃×C₆²	108		(C3xC6^2):1C2	216,151
(C₃×C₆²)⋊₂C₂ = C₃²×C₃⋊D₄	φ: C₂/C₁ → C₂ ⊆ Aut C₃×C₆²	36		(C3xC6^2):2C2	216,139
(C₃×C₆²)⋊₃C₂ = C₃×C₃²⋊₇D₄	φ: C₂/C₁ → C₂ ⊆ Aut C₃×C₆²	36		(C3xC6^2):3C2	216,144
(C₃×C₆²)⋊₄C₂ = C₃³⋊₁₅D₄	φ: C₂/C₁ → C₂ ⊆ Aut C₃×C₆²	108		(C3xC6^2):4C2	216,149
(C₃×C₆²)⋊₅C₂ = S₃×C₆²	φ: C₂/C₁ → C₂ ⊆ Aut C₃×C₆²	72		(C3xC6^2):5C2	216,174
(C₃×C₆²)⋊₆C₂ = C₂×C₆×C₃⋊S₃	φ: C₂/C₁ → C₂ ⊆ Aut C₃×C₆²	72		(C3xC6^2):6C2	216,175
(C₃×C₆²)⋊₇C₂ = C₂²×C₃³⋊C₂	φ: C₂/C₁ → C₂ ⊆ Aut C₃×C₆²	108		(C3xC6^2):7C2	216,176

Non-split extensions G=N.Q with N=C₃×C₆² and Q=C₂

extension	φ:Q→Aut N	d	ρ	Label	ID
(C₃×C₆²).₁C₂ = Dic₃×C₃×C₆	φ: C₂/C₁ → C₂ ⊆ Aut C₃×C₆²	72		(C3xC6^2).1C2	216,138
(C₃×C₆²).₂C₂ = C₆×C₃⋊Dic₃	φ: C₂/C₁ → C₂ ⊆ Aut C₃×C₆²	72		(C3xC6^2).2C2	216,143
(C₃×C₆²).₃C₂ = C₂×C₃³⋊₅C₄	φ: C₂/C₁ → C₂ ⊆ Aut C₃×C₆²	216		(C3xC6^2).3C2	216,148

׿

×

⋊

ℤ

𝔽

○

≀

ℚ

◁