Extensions 1→N→G→Q→1 with N=C₆ and Q=C₂×C₁₄

Direct product G=N×Q with N=C₆ and Q=C₂×C₁₄

		d	ρ	Label	ID
C₂²×C₄₂		168		C2^2xC42	168,57

Semidirect products G=N:Q with N=C₆ and Q=C₂×C₁₄

extension	φ:Q→Aut N	d	ρ	Label	ID
C₆⋊(C₂×C₁₄) = S₃×C₂×C₁₄	φ: C₂×C₁₄/C₁₄ → C₂ ⊆ Aut C₆	84		C6:(C2xC14)	168,55

Non-split extensions G=N.Q with N=C₆ and Q=C₂×C₁₄

extension	φ:Q→Aut N	d	ρ	Label	ID
C₆.₁(C₂×C₁₄) = C₇×Dic₆	φ: C₂×C₁₄/C₁₄ → C₂ ⊆ Aut C₆	168	2	C6.1(C2xC14)	168,29
C₆.₂(C₂×C₁₄) = S₃×C₂₈	φ: C₂×C₁₄/C₁₄ → C₂ ⊆ Aut C₆	84	2	C6.2(C2xC14)	168,30
C₆.₃(C₂×C₁₄) = C₇×D₁₂	φ: C₂×C₁₄/C₁₄ → C₂ ⊆ Aut C₆	84	2	C6.3(C2xC14)	168,31
C₆.₄(C₂×C₁₄) = Dic₃×C₁₄	φ: C₂×C₁₄/C₁₄ → C₂ ⊆ Aut C₆	168		C6.4(C2xC14)	168,32
C₆.₅(C₂×C₁₄) = C₇×C₃⋊D₄	φ: C₂×C₁₄/C₁₄ → C₂ ⊆ Aut C₆	84	2	C6.5(C2xC14)	168,33
C₆.₆(C₂×C₁₄) = D₄×C₂₁	central extension (φ=1)	84	2	C6.6(C2xC14)	168,40
C₆.₇(C₂×C₁₄) = Q₈×C₂₁	central extension (φ=1)	168	2	C6.7(C2xC14)	168,41

׿

×

⋊

ℤ

𝔽

○

≀

ℚ

◁