Extensions 1→N→G→Q→1 with N=C₁₄ and Q=D₄

Direct product G=N×Q with N=C₁₄ and Q=D₄

		d	ρ	Label	ID
D₄×C₁₄		56		D4xC14	112,38

Semidirect products G=N:Q with N=C₁₄ and Q=D₄

extension	φ:Q→Aut N	d	ρ	Label	ID
C₁₄⋊₁D₄ = C₂×D₂₈	φ: D₄/C₄ → C₂ ⊆ Aut C₁₄	56		C14:1D4	112,29
C₁₄⋊₂D₄ = C₂×C₇⋊D₄	φ: D₄/C₂² → C₂ ⊆ Aut C₁₄	56		C14:2D4	112,36

Non-split extensions G=N.Q with N=C₁₄ and Q=D₄

extension	φ:Q→Aut N	d	ρ	Label	ID
C₁₄.₁D₄ = C₅₆⋊C₂	φ: D₄/C₄ → C₂ ⊆ Aut C₁₄	56	2	C14.1D4	112,5
C₁₄.₂D₄ = D₅₆	φ: D₄/C₄ → C₂ ⊆ Aut C₁₄	56	2+	C14.2D4	112,6
C₁₄.₃D₄ = Dic₂₈	φ: D₄/C₄ → C₂ ⊆ Aut C₁₄	112	2-	C14.3D4	112,7
C₁₄.₄D₄ = C₄⋊Dic₇	φ: D₄/C₄ → C₂ ⊆ Aut C₁₄	112		C14.4D4	112,12
C₁₄.₅D₄ = Dic₇⋊C₄	φ: D₄/C₂² → C₂ ⊆ Aut C₁₄	112		C14.5D4	112,11
C₁₄.₆D₄ = D₁₄⋊C₄	φ: D₄/C₂² → C₂ ⊆ Aut C₁₄	56		C14.6D4	112,13
C₁₄.₇D₄ = D₄⋊D₇	φ: D₄/C₂² → C₂ ⊆ Aut C₁₄	56	4+	C14.7D4	112,14
C₁₄.₈D₄ = D₄.D₇	φ: D₄/C₂² → C₂ ⊆ Aut C₁₄	56	4-	C14.8D4	112,15
C₁₄.₉D₄ = Q₈⋊D₇	φ: D₄/C₂² → C₂ ⊆ Aut C₁₄	56	4+	C14.9D4	112,16
C₁₄.₁₀D₄ = C₇⋊Q₁₆	φ: D₄/C₂² → C₂ ⊆ Aut C₁₄	112	4-	C14.10D4	112,17
C₁₄.₁₁D₄ = C₂³.D₇	φ: D₄/C₂² → C₂ ⊆ Aut C₁₄	56		C14.11D4	112,18
C₁₄.₁₂D₄ = C₇×C₂²⋊C₄	central extension (φ=1)	56		C14.12D4	112,20
C₁₄.₁₃D₄ = C₇×C₄⋊C₄	central extension (φ=1)	112		C14.13D4	112,21
C₁₄.₁₄D₄ = C₇×D₈	central extension (φ=1)	56	2	C14.14D4	112,24
C₁₄.₁₅D₄ = C₇×SD₁₆	central extension (φ=1)	56	2	C14.15D4	112,25
C₁₄.₁₆D₄ = C₇×Q₁₆	central extension (φ=1)	112	2	C14.16D4	112,26

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