Extensions 1→N→G→Q→1 with N=C₂³ and Q=C₂×C₁₄

Direct product G=N×Q with N=C₂³ and Q=C₂×C₁₄

		d	ρ	Label	ID
C₂⁴×C₁₄		224		C2^4xC14	224,197

Semidirect products G=N:Q with N=C₂³ and Q=C₂×C₁₄

extension	φ:Q→Aut N	d	ρ	Label	ID
C₂³⋊(C₂×C₁₄) = C₂²×F₈	φ: C₂×C₁₄/C₂² → C₇ ⊆ Aut C₂³	28		C2^3:(C2xC14)	224,195
C₂³⋊₂(C₂×C₁₄) = C₇×C₂²≀C₂	φ: C₂×C₁₄/C₇ → C₂² ⊆ Aut C₂³	56		C2^3:2(C2xC14)	224,155
C₂³⋊₃(C₂×C₁₄) = C₇×2₊¹⁺⁴	φ: C₂×C₁₄/C₇ → C₂² ⊆ Aut C₂³	56	4	C2^3:3(C2xC14)	224,193
C₂³⋊₄(C₂×C₁₄) = D₄×C₂×C₁₄	φ: C₂×C₁₄/C₁₄ → C₂ ⊆ Aut C₂³	112		C2^3:4(C2xC14)	224,190

Non-split extensions G=N.Q with N=C₂³ and Q=C₂×C₁₄

extension	φ:Q→Aut N	d	ρ	Label	ID
C₂³.₁(C₂×C₁₄) = C₇×C₂³⋊C₄	φ: C₂×C₁₄/C₇ → C₂² ⊆ Aut C₂³	56	4	C2^3.1(C2xC14)	224,48
C₂³.₂(C₂×C₁₄) = C₇×C₄.₄D₄	φ: C₂×C₁₄/C₇ → C₂² ⊆ Aut C₂³	112		C2^3.2(C2xC14)	224,159
C₂³.₃(C₂×C₁₄) = C₇×C₄²⋊₂C₂	φ: C₂×C₁₄/C₇ → C₂² ⊆ Aut C₂³	112		C2^3.3(C2xC14)	224,161
C₂³.₄(C₂×C₁₄) = C₇×C₄⋊₁D₄	φ: C₂×C₁₄/C₇ → C₂² ⊆ Aut C₂³	112		C2^3.4(C2xC14)	224,162
C₂³.₅(C₂×C₁₄) = C₁₄×C₂²⋊C₄	φ: C₂×C₁₄/C₁₄ → C₂ ⊆ Aut C₂³	112		C2^3.5(C2xC14)	224,150
C₂³.₆(C₂×C₁₄) = C₇×C₄²⋊C₂	φ: C₂×C₁₄/C₁₄ → C₂ ⊆ Aut C₂³	112		C2^3.6(C2xC14)	224,152
C₂³.₇(C₂×C₁₄) = D₄×C₂₈	φ: C₂×C₁₄/C₁₄ → C₂ ⊆ Aut C₂³	112		C2^3.7(C2xC14)	224,153
C₂³.₈(C₂×C₁₄) = C₇×C₄⋊D₄	φ: C₂×C₁₄/C₁₄ → C₂ ⊆ Aut C₂³	112		C2^3.8(C2xC14)	224,156
C₂³.₉(C₂×C₁₄) = C₇×C₂²⋊Q₈	φ: C₂×C₁₄/C₁₄ → C₂ ⊆ Aut C₂³	112		C2^3.9(C2xC14)	224,157
C₂³.₁₀(C₂×C₁₄) = C₇×C₂².D₄	φ: C₂×C₁₄/C₁₄ → C₂ ⊆ Aut C₂³	112		C2^3.10(C2xC14)	224,158
C₂³.₁₁(C₂×C₁₄) = C₁₄×C₄○D₄	φ: C₂×C₁₄/C₁₄ → C₂ ⊆ Aut C₂³	112		C2^3.11(C2xC14)	224,192
C₂³.₁₂(C₂×C₁₄) = C₇×C₂.C₄²	central extension (φ=1)	224		C2^3.12(C2xC14)	224,44
C₂³.₁₃(C₂×C₁₄) = C₁₄×C₄⋊C₄	central extension (φ=1)	224		C2^3.13(C2xC14)	224,151
C₂³.₁₄(C₂×C₁₄) = Q₈×C₂×C₁₄	central extension (φ=1)	224		C2^3.14(C2xC14)	224,191

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