Extensions 1→N→G→Q→1 with N=C₂₁₆ and Q=C₂

Direct product G=N×Q with N=C₂₁₆ and Q=C₂

		d	ρ	Label	ID
C₂×C₂₁₆		432		C2xC216	432,23

Semidirect products G=N:Q with N=C₂₁₆ and Q=C₂

extension	φ:Q→Aut N	d	ρ	Label	ID
C₂₁₆⋊₁C₂ = D₂₁₆	φ: C₂/C₁ → C₂ ⊆ Aut C₂₁₆	216	2+	C216:1C2	432,8
C₂₁₆⋊₂C₂ = C₂₁₆⋊C₂	φ: C₂/C₁ → C₂ ⊆ Aut C₂₁₆	216	2	C216:2C2	432,7
C₂₁₆⋊₃C₂ = C₈×D₂₇	φ: C₂/C₁ → C₂ ⊆ Aut C₂₁₆	216	2	C216:3C2	432,5
C₂₁₆⋊₄C₂ = C₈⋊D₂₇	φ: C₂/C₁ → C₂ ⊆ Aut C₂₁₆	216	2	C216:4C2	432,6
C₂₁₆⋊₅C₂ = D₈×C₂₇	φ: C₂/C₁ → C₂ ⊆ Aut C₂₁₆	216	2	C216:5C2	432,25
C₂₁₆⋊₆C₂ = SD₁₆×C₂₇	φ: C₂/C₁ → C₂ ⊆ Aut C₂₁₆	216	2	C216:6C2	432,26
C₂₁₆⋊₇C₂ = M₄(2)×C₂₇	φ: C₂/C₁ → C₂ ⊆ Aut C₂₁₆	216	2	C216:7C2	432,24

Non-split extensions G=N.Q with N=C₂₁₆ and Q=C₂

extension	φ:Q→Aut N	d	ρ	Label	ID
C₂₁₆.₁C₂ = Dic₁₀₈	φ: C₂/C₁ → C₂ ⊆ Aut C₂₁₆	432	2-	C216.1C2	432,4
C₂₁₆.₂C₂ = C₂₇⋊C₁₆	φ: C₂/C₁ → C₂ ⊆ Aut C₂₁₆	432	2	C216.2C2	432,1
C₂₁₆.₃C₂ = Q₁₆×C₂₇	φ: C₂/C₁ → C₂ ⊆ Aut C₂₁₆	432	2	C216.3C2	432,27

׿

×

⋊

ℤ

𝔽

○

≀

ℚ

◁