Extensions 1→N→G→Q→1 with N=D₄ and Q=C₂×C₇⋊C₃

Direct product G=N×Q with N=D₄ and Q=C₂×C₇⋊C₃

		d	ρ	Label	ID
C₂×D₄×C₇⋊C₃		56		C2xD4xC7:C3	336,165

Semidirect products G=N:Q with N=D₄ and Q=C₂×C₇⋊C₃

extension	φ:Q→Out N	d	ρ	Label	ID
D₄⋊(C₂×C₇⋊C₃) = D₈×C₇⋊C₃	φ: C₂×C₇⋊C₃/C₇⋊C₃ → C₂ ⊆ Out D₄	56	6	D4:(C2xC7:C3)	336,53
D₄⋊₂(C₂×C₇⋊C₃) = C₄○D₄×C₇⋊C₃	φ: trivial image	56	6	D4:2(C2xC7:C3)	336,167

Non-split extensions G=N.Q with N=D₄ and Q=C₂×C₇⋊C₃

extension	φ:Q→Out N	d	ρ	Label	ID
D₄.(C₂×C₇⋊C₃) = SD₁₆×C₇⋊C₃	φ: C₂×C₇⋊C₃/C₇⋊C₃ → C₂ ⊆ Out D₄	56	6	D4.(C2xC7:C3)	336,54

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Extensions 1→N→G→Q→1 with N=D4 and Q=C2×C7⋊C3