Extensions 1→N→G→Q→1 with N=C₇ and Q=C₃×C₄○D₄

Direct product G=N×Q with N=C₇ and Q=C₃×C₄○D₄

		d	ρ	Label	ID
C₄○D₄×C₂₁		168	2	C4oD4xC21	336,207

Semidirect products G=N:Q with N=C₇ and Q=C₃×C₄○D₄

extension	φ:Q→Aut N	d	ρ	Label	ID
C₇⋊₁(C₃×C₄○D₄) = D₂₈⋊₆C₆	φ: C₃×C₄○D₄/C₂×C₄ → C₆ ⊆ Aut C₇	56	6	C7:1(C3xC4oD4)	336,124
C₇⋊₂(C₃×C₄○D₄) = D₄⋊₂F₇	φ: C₃×C₄○D₄/D₄ → C₆ ⊆ Aut C₇	56	12-	C7:2(C3xC4oD4)	336,126
C₇⋊₃(C₃×C₄○D₄) = Q₈⋊₃F₇	φ: C₃×C₄○D₄/Q₈ → C₆ ⊆ Aut C₇	56	12+	C7:3(C3xC4oD4)	336,128
C₇⋊₄(C₃×C₄○D₄) = C₄○D₄×C₇⋊C₃	φ: C₃×C₄○D₄/C₄○D₄ → C₃ ⊆ Aut C₇	56	6	C7:4(C3xC4oD4)	336,167
C₇⋊₅(C₃×C₄○D₄) = C₃×C₄○D₂₈	φ: C₃×C₄○D₄/C₂×C₁₂ → C₂ ⊆ Aut C₇	168	2	C7:5(C3xC4oD4)	336,177
C₇⋊₆(C₃×C₄○D₄) = C₃×D₄⋊₂D₇	φ: C₃×C₄○D₄/C₃×D₄ → C₂ ⊆ Aut C₇	168	4	C7:6(C3xC4oD4)	336,179
C₇⋊₇(C₃×C₄○D₄) = C₃×Q₈⋊₂D₇	φ: C₃×C₄○D₄/C₃×Q₈ → C₂ ⊆ Aut C₇	168	4	C7:7(C3xC4oD4)	336,181

׿

×

⋊

ℤ

𝔽

○

≀

ℚ

◁