Extensions 1→N→G→Q→1 with N=C₇ and Q=C₇⋊D₄

Direct product G=N×Q with N=C₇ and Q=C₇⋊D₄

		d	ρ	Label	ID
C₇×C₇⋊D₄		28	2	C7xC7:D4	392,27

Semidirect products G=N:Q with N=C₇ and Q=C₇⋊D₄

extension	φ:Q→Aut N	d	ρ	Label	ID
C₇⋊₁(C₇⋊D₄) = C₇⋊D₂₈	φ: C₇⋊D₄/Dic₇ → C₂ ⊆ Aut C₇	28	4+	C7:1(C7:D4)	392,21
C₇⋊₂(C₇⋊D₄) = C₇²⋊₂D₄	φ: C₇⋊D₄/D₁₄ → C₂ ⊆ Aut C₇	56	4-	C7:2(C7:D4)	392,20
C₇⋊₃(C₇⋊D₄) = C₇²⋊₇D₄	φ: C₇⋊D₄/C₂×C₁₄ → C₂ ⊆ Aut C₇	196		C7:3(C7:D4)	392,32

Non-split extensions G=N.Q with N=C₇ and Q=C₇⋊D₄

extension	φ:Q→Aut N	d	ρ	Label	ID
C₇.(C₇⋊D₄) = C₄₉⋊D₄	φ: C₇⋊D₄/C₂×C₁₄ → C₂ ⊆ Aut C₇	196	2	C7.(C7:D4)	392,7

⋊

ℤ

𝔽

○

≀

ℚ

◁

Extensions 1→N→G→Q→1 with N=C7 and Q=C7⋊D4