Extensions 1→N→G→Q→1 with N=C₄⋊₁D₄ and Q=D₇

Direct product G=N×Q with N=C₄⋊₁D₄ and Q=D₇

		d	ρ	Label	ID
D₇×C₄⋊₁D₄		112		D7xC4:1D4	448,1167

Semidirect products G=N:Q with N=C₄⋊₁D₄ and Q=D₇

extension	φ:Q→Out N	d	ρ	Label	ID
C₄⋊₁D₄⋊₁D₇ = C₂₈⋊₂D₈	φ: D₇/C₇ → C₂ ⊆ Out C₄⋊₁D₄	224		C4:1D4:1D7	448,606
C₄⋊₁D₄⋊₂D₇ = C₂₈⋊D₈	φ: D₇/C₇ → C₂ ⊆ Out C₄⋊₁D₄	224		C4:1D4:2D7	448,607
C₄⋊₁D₄⋊₃D₇ = C₄².₇₄D₁₄	φ: D₇/C₇ → C₂ ⊆ Out C₄⋊₁D₄	224		C4:1D4:3D7	448,608
C₄⋊₁D₄⋊₄D₇ = D₂₈⋊₅D₄	φ: D₇/C₇ → C₂ ⊆ Out C₄⋊₁D₄	56	4	C4:1D4:4D7	448,611
C₄⋊₁D₄⋊₅D₇ = C₄²⋊₂₆D₁₄	φ: D₇/C₇ → C₂ ⊆ Out C₄⋊₁D₄	112		C4:1D4:5D7	448,1168
C₄⋊₁D₄⋊₆D₇ = D₂₈⋊₁₁D₄	φ: D₇/C₇ → C₂ ⊆ Out C₄⋊₁D₄	112		C4:1D4:6D7	448,1170
C₄⋊₁D₄⋊₇D₇ = Dic₁₄⋊₁₁D₄	φ: D₇/C₇ → C₂ ⊆ Out C₄⋊₁D₄	224		C4:1D4:7D7	448,1171
C₄⋊₁D₄⋊₈D₇ = C₄².₁₆₈D₁₄	φ: D₇/C₇ → C₂ ⊆ Out C₄⋊₁D₄	224		C4:1D4:8D7	448,1172
C₄⋊₁D₄⋊₉D₇ = C₄²⋊₂₈D₁₄	φ: D₇/C₇ → C₂ ⊆ Out C₄⋊₁D₄	112		C4:1D4:9D7	448,1173
C₄⋊₁D₄⋊₁₀D₇ = C₄².₂₃₈D₁₄	φ: trivial image	224		C4:1D4:10D7	448,1169

Non-split extensions G=N.Q with N=C₄⋊₁D₄ and Q=D₇

extension	φ:Q→Out N	d	ρ	Label	ID
C₄⋊₁D₄.₁D₇ = C₂₈.₉D₈	φ: D₇/C₇ → C₂ ⊆ Out C₄⋊₁D₄	224		C4:1D4.1D7	448,101
C₄⋊₁D₄.₂D₇ = C₄²⋊₃Dic₇	φ: D₇/C₇ → C₂ ⊆ Out C₄⋊₁D₄	56	4	C4:1D4.2D7	448,102
C₄⋊₁D₄.₃D₇ = C₂₈.₁₆D₈	φ: D₇/C₇ → C₂ ⊆ Out C₄⋊₁D₄	224		C4:1D4.3D7	448,604
C₄⋊₁D₄.₄D₇ = C₄².₇₂D₁₄	φ: D₇/C₇ → C₂ ⊆ Out C₄⋊₁D₄	224		C4:1D4.4D7	448,605
C₄⋊₁D₄.₅D₇ = Dic₁₄⋊₉D₄	φ: D₇/C₇ → C₂ ⊆ Out C₄⋊₁D₄	224		C4:1D4.5D7	448,609
C₄⋊₁D₄.₆D₇ = C₂₈⋊₄SD₁₆	φ: D₇/C₇ → C₂ ⊆ Out C₄⋊₁D₄	224		C4:1D4.6D7	448,610
C₄⋊₁D₄.₇D₇ = C₄².₁₆₆D₁₄	φ: D₇/C₇ → C₂ ⊆ Out C₄⋊₁D₄	224		C4:1D4.7D7	448,1166

׿

×

⋊

ℤ

𝔽

○

≀

ℚ

◁