Extensions 1→N→G→Q→1 with N=C₇ and Q=C₂×C₂²⋊Q₈

Direct product G=N×Q with N=C₇ and Q=C₂×C₂²⋊Q₈

		d	ρ	Label	ID
C₁₄×C₂²⋊Q₈		224		C14xC2^2:Q8	448,1306

Semidirect products G=N:Q with N=C₇ and Q=C₂×C₂²⋊Q₈

extension	φ:Q→Aut N	d	ρ	Label	ID
C₇⋊₁(C₂×C₂²⋊Q₈) = C₂×C₂²⋊Dic₁₄	φ: C₂×C₂²⋊Q₈/C₂×C₂²⋊C₄ → C₂ ⊆ Aut C₇	224		C7:1(C2xC2^2:Q8)	448,934
C₇⋊₂(C₂×C₂²⋊Q₈) = C₂×D₁₄⋊Q₈	φ: C₂×C₂²⋊Q₈/C₂×C₄⋊C₄ → C₂ ⊆ Aut C₇	224		C7:2(C2xC2^2:Q8)	448,961
C₇⋊₃(C₂×C₂²⋊Q₈) = C₂×D₁₄⋊₂Q₈	φ: C₂×C₂²⋊Q₈/C₂×C₄⋊C₄ → C₂ ⊆ Aut C₇	224		C7:3(C2xC2^2:Q8)	448,962
C₇⋊₄(C₂×C₂²⋊Q₈) = D₇×C₂²⋊Q₈	φ: C₂×C₂²⋊Q₈/C₂²⋊Q₈ → C₂ ⊆ Aut C₇	112		C7:4(C2xC2^2:Q8)	448,1079
C₇⋊₅(C₂×C₂²⋊Q₈) = C₂×C₂₈.₄₈D₄	φ: C₂×C₂²⋊Q₈/C₂³×C₄ → C₂ ⊆ Aut C₇	224		C7:5(C2xC2^2:Q8)	448,1237
C₇⋊₆(C₂×C₂²⋊Q₈) = C₂×D₁₄⋊₃Q₈	φ: C₂×C₂²⋊Q₈/C₂²×Q₈ → C₂ ⊆ Aut C₇	224		C7:6(C2xC2^2:Q8)	448,1266

׿

×

⋊

ℤ

𝔽

○

≀

ℚ

◁