Extensions 1→N→G→Q→1 with N=C₄ and Q=S₃×C₇

Direct product G=N×Q with N=C₄ and Q=S₃×C₇

		d	ρ	Label	ID
S₃×C₂₈		84	2	S3xC28	168,30

Semidirect products G=N:Q with N=C₄ and Q=S₃×C₇

extension	φ:Q→Aut N	d	ρ	Label	ID
C₄⋊(S₃×C₇) = C₇×D₁₂	φ: S₃×C₇/C₂₁ → C₂ ⊆ Aut C₄	84	2	C4:(S3xC7)	168,31

Non-split extensions G=N.Q with N=C₄ and Q=S₃×C₇

extension	φ:Q→Aut N	d	ρ	Label	ID
C₄.(S₃×C₇) = C₇×Dic₆	φ: S₃×C₇/C₂₁ → C₂ ⊆ Aut C₄	168	2	C4.(S3xC7)	168,29
C₄.₂(S₃×C₇) = C₇×C₃⋊C₈	central extension (φ=1)	168	2	C4.2(S3xC7)	168,3

⋊

ℤ

𝔽

○

≀

ℚ

◁

Extensions 1→N→G→Q→1 with N=C4 and Q=S3×C7