Extensions 1→N→G→Q→1 with N=C₇ and Q=C₃×Q₈

Direct product G=N×Q with N=C₇ and Q=C₃×Q₈

		d	ρ	Label	ID
Q₈×C₂₁		168	2	Q8xC21	168,41

Semidirect products G=N:Q with N=C₇ and Q=C₃×Q₈

extension	φ:Q→Aut N	d	ρ	Label	ID
C₇⋊(C₃×Q₈) = C₄.F₇	φ: C₃×Q₈/C₄ → C₆ ⊆ Aut C₇	56	6-	C7:(C3xQ8)	168,7
C₇⋊₂(C₃×Q₈) = Q₈×C₇⋊C₃	φ: C₃×Q₈/Q₈ → C₃ ⊆ Aut C₇	56	6	C7:2(C3xQ8)	168,21
C₇⋊₃(C₃×Q₈) = C₃×Dic₁₄	φ: C₃×Q₈/C₁₂ → C₂ ⊆ Aut C₇	168	2	C7:3(C3xQ8)	168,24

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