Extensions 1→N→G→Q→1 with N=C₄ and Q=C₃×D₇

Direct product G=N×Q with N=C₄ and Q=C₃×D₇

		d	ρ	Label	ID
C₁₂×D₇		84	2	C12xD7	168,25

Semidirect products G=N:Q with N=C₄ and Q=C₃×D₇

extension	φ:Q→Aut N	d	ρ	Label	ID
C₄⋊(C₃×D₇) = C₃×D₂₈	φ: C₃×D₇/C₂₁ → C₂ ⊆ Aut C₄	84	2	C4:(C3xD7)	168,26

Non-split extensions G=N.Q with N=C₄ and Q=C₃×D₇

extension	φ:Q→Aut N	d	ρ	Label	ID
C₄.(C₃×D₇) = C₃×Dic₁₄	φ: C₃×D₇/C₂₁ → C₂ ⊆ Aut C₄	168	2	C4.(C3xD7)	168,24
C₄.₂(C₃×D₇) = C₃×C₇⋊C₈	central extension (φ=1)	168	2	C4.2(C3xD7)	168,4

⋊

ℤ

𝔽

○

≀

ℚ

◁

Extensions 1→N→G→Q→1 with N=C4 and Q=C3×D7