Extensions 1→N→G→Q→1 with N=C₂×C₆₈ and Q=C₂

Direct product G=N×Q with N=C₂×C₆₈ and Q=C₂

		d	ρ	Label	ID
C₂²×C₆₈		272		C2^2xC68	272,46

Semidirect products G=N:Q with N=C₂×C₆₈ and Q=C₂

extension	φ:Q→Aut N	d	ρ	Label	ID
(C₂×C₆₈)⋊₁C₂ = D₃₄⋊C₄	φ: C₂/C₁ → C₂ ⊆ Aut C₂×C₆₈	136		(C2xC68):1C2	272,14
(C₂×C₆₈)⋊₂C₂ = C₂²⋊C₄×C₁₇	φ: C₂/C₁ → C₂ ⊆ Aut C₂×C₆₈	136		(C2xC68):2C2	272,21
(C₂×C₆₈)⋊₃C₂ = C₂×D₆₈	φ: C₂/C₁ → C₂ ⊆ Aut C₂×C₆₈	136		(C2xC68):3C2	272,38
(C₂×C₆₈)⋊₄C₂ = D₆₈⋊₅C₂	φ: C₂/C₁ → C₂ ⊆ Aut C₂×C₆₈	136	2	(C2xC68):4C2	272,39
(C₂×C₆₈)⋊₅C₂ = C₂×C₄×D₁₇	φ: C₂/C₁ → C₂ ⊆ Aut C₂×C₆₈	136		(C2xC68):5C2	272,37
(C₂×C₆₈)⋊₆C₂ = D₄×C₃₄	φ: C₂/C₁ → C₂ ⊆ Aut C₂×C₆₈	136		(C2xC68):6C2	272,47
(C₂×C₆₈)⋊₇C₂ = C₄○D₄×C₁₇	φ: C₂/C₁ → C₂ ⊆ Aut C₂×C₆₈	136	2	(C2xC68):7C2	272,49

Non-split extensions G=N.Q with N=C₂×C₆₈ and Q=C₂

extension	φ:Q→Aut N	d	ρ	Label	ID
(C₂×C₆₈).₁C₂ = C₃₄.D₄	φ: C₂/C₁ → C₂ ⊆ Aut C₂×C₆₈	272		(C2xC68).1C2	272,12
(C₂×C₆₈).₂C₂ = C₄⋊C₄×C₁₇	φ: C₂/C₁ → C₂ ⊆ Aut C₂×C₆₈	272		(C2xC68).2C2	272,22
(C₂×C₆₈).₃C₂ = C₆₈⋊₃C₄	φ: C₂/C₁ → C₂ ⊆ Aut C₂×C₆₈	272		(C2xC68).3C2	272,13
(C₂×C₆₈).₄C₂ = C₂×Dic₃₄	φ: C₂/C₁ → C₂ ⊆ Aut C₂×C₆₈	272		(C2xC68).4C2	272,36
(C₂×C₆₈).₅C₂ = C₆₈.₄C₄	φ: C₂/C₁ → C₂ ⊆ Aut C₂×C₆₈	136	2	(C2xC68).5C2	272,10
(C₂×C₆₈).₆C₂ = C₂×C₁₇⋊₃C₈	φ: C₂/C₁ → C₂ ⊆ Aut C₂×C₆₈	272		(C2xC68).6C2	272,9
(C₂×C₆₈).₇C₂ = C₄×Dic₁₇	φ: C₂/C₁ → C₂ ⊆ Aut C₂×C₆₈	272		(C2xC68).7C2	272,11
(C₂×C₆₈).₈C₂ = M₄(2)×C₁₇	φ: C₂/C₁ → C₂ ⊆ Aut C₂×C₆₈	136	2	(C2xC68).8C2	272,24
(C₂×C₆₈).₉C₂ = Q₈×C₃₄	φ: C₂/C₁ → C₂ ⊆ Aut C₂×C₆₈	272		(C2xC68).9C2	272,48

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