Extensions 1→N→G→Q→1 with N=C₂₄ and Q=C₁₄

Direct product G=N×Q with N=C₂₄ and Q=C₁₄

		d	ρ	Label	ID
C₂×C₁₆₈		336		C2xC168	336,109

Semidirect products G=N:Q with N=C₂₄ and Q=C₁₄

extension	φ:Q→Aut N	d	ρ	Label	ID
C₂₄⋊₁C₁₄ = C₇×D₂₄	φ: C₁₄/C₇ → C₂ ⊆ Aut C₂₄	168	2	C24:1C14	336,77
C₂₄⋊₂C₁₄ = C₇×C₂₄⋊C₂	φ: C₁₄/C₇ → C₂ ⊆ Aut C₂₄	168	2	C24:2C14	336,76
C₂₄⋊₃C₁₄ = D₈×C₂₁	φ: C₁₄/C₇ → C₂ ⊆ Aut C₂₄	168	2	C24:3C14	336,111
C₂₄⋊₄C₁₄ = S₃×C₅₆	φ: C₁₄/C₇ → C₂ ⊆ Aut C₂₄	168	2	C24:4C14	336,74
C₂₄⋊₅C₁₄ = C₇×C₈⋊S₃	φ: C₁₄/C₇ → C₂ ⊆ Aut C₂₄	168	2	C24:5C14	336,75
C₂₄⋊₆C₁₄ = SD₁₆×C₂₁	φ: C₁₄/C₇ → C₂ ⊆ Aut C₂₄	168	2	C24:6C14	336,112
C₂₄⋊₇C₁₄ = M₄(2)×C₂₁	φ: C₁₄/C₇ → C₂ ⊆ Aut C₂₄	168	2	C24:7C14	336,110

Non-split extensions G=N.Q with N=C₂₄ and Q=C₁₄

extension	φ:Q→Aut N	d	ρ	Label	ID
C₂₄.₁C₁₄ = C₇×Dic₁₂	φ: C₁₄/C₇ → C₂ ⊆ Aut C₂₄	336	2	C24.1C14	336,78
C₂₄.₂C₁₄ = Q₁₆×C₂₁	φ: C₁₄/C₇ → C₂ ⊆ Aut C₂₄	336	2	C24.2C14	336,113
C₂₄.₃C₁₄ = C₇×C₃⋊C₁₆	φ: C₁₄/C₇ → C₂ ⊆ Aut C₂₄	336	2	C24.3C14	336,3

׿

×

⋊

ℤ

𝔽

○

≀

ℚ

◁