Extensions 1→N→G→Q→1 with N=C₆ and Q=C₂×C₁₃⋊C₃

Direct product G=N×Q with N=C₆ and Q=C₂×C₁₃⋊C₃

		d	ρ	Label	ID
C₂×C₆×C₁₃⋊C₃		156		C2xC6xC13:C3	468,47

Semidirect products G=N:Q with N=C₆ and Q=C₂×C₁₃⋊C₃

extension	φ:Q→Aut N	d	ρ	Label	ID
C₆⋊(C₂×C₁₃⋊C₃) = C₂×S₃×C₁₃⋊C₃	φ: C₂×C₁₃⋊C₃/C₁₃⋊C₃ → C₂ ⊆ Aut C₆	78	6	C6:(C2xC13:C3)	468,34

Non-split extensions G=N.Q with N=C₆ and Q=C₂×C₁₃⋊C₃

extension	φ:Q→Aut N	d	ρ	Label	ID
C₆.(C₂×C₁₃⋊C₃) = Dic₃×C₁₃⋊C₃	φ: C₂×C₁₃⋊C₃/C₁₃⋊C₃ → C₂ ⊆ Aut C₆	156	6	C6.(C2xC13:C3)	468,20
C₆.₂(C₂×C₁₃⋊C₃) = C₄×C₁₃⋊C₉	central extension (φ=1)	468	3	C6.2(C2xC13:C3)	468,2
C₆.₃(C₂×C₁₃⋊C₃) = C₂²×C₁₃⋊C₉	central extension (φ=1)	468		C6.3(C2xC13:C3)	468,12
C₆.₄(C₂×C₁₃⋊C₃) = C₁₂×C₁₃⋊C₃	central extension (φ=1)	156	3	C6.4(C2xC13:C3)	468,22

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