Extensions 1→N→G→Q→1 with N=C₆₈ and Q=C₆

Direct product G=N×Q with N=C₆₈ and Q=C₆

		d	ρ	Label	ID
C₂×C₂₀₄		408		C2xC204	408,30

Semidirect products G=N:Q with N=C₆₈ and Q=C₆

extension	φ:Q→Aut N	d	ρ	Label	ID
C₆₈⋊₁C₆ = C₃×D₆₈	φ: C₆/C₃ → C₂ ⊆ Aut C₆₈	204	2	C68:1C6	408,17
C₆₈⋊₂C₆ = C₁₂×D₁₇	φ: C₆/C₃ → C₂ ⊆ Aut C₆₈	204	2	C68:2C6	408,16
C₆₈⋊₃C₆ = D₄×C₅₁	φ: C₆/C₃ → C₂ ⊆ Aut C₆₈	204	2	C68:3C6	408,31

Non-split extensions G=N.Q with N=C₆₈ and Q=C₆

extension	φ:Q→Aut N	d	ρ	Label	ID
C₆₈.₁C₆ = C₃×Dic₃₄	φ: C₆/C₃ → C₂ ⊆ Aut C₆₈	408	2	C68.1C6	408,15
C₆₈.₂C₆ = C₃×C₁₇⋊₃C₈	φ: C₆/C₃ → C₂ ⊆ Aut C₆₈	408	2	C68.2C6	408,2
C₆₈.₃C₆ = Q₈×C₅₁	φ: C₆/C₃ → C₂ ⊆ Aut C₆₈	408	2	C68.3C6	408,32

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Extensions 1→N→G→Q→1 with N=C68 and Q=C6