Extensions 1→N→G→Q→1 with N=C₂₂ and Q=D₄

Direct product G=N×Q with N=C₂₂ and Q=D₄

		d	ρ	Label	ID
D₄×C₂₂		88		D4xC22	176,38

Semidirect products G=N:Q with N=C₂₂ and Q=D₄

extension	φ:Q→Aut N	d	ρ	Label	ID
C₂₂⋊₁D₄ = C₂×D₄₄	φ: D₄/C₄ → C₂ ⊆ Aut C₂₂	88		C22:1D4	176,29
C₂₂⋊₂D₄ = C₂×C₁₁⋊D₄	φ: D₄/C₂² → C₂ ⊆ Aut C₂₂	88		C22:2D4	176,36

Non-split extensions G=N.Q with N=C₂₂ and Q=D₄

extension	φ:Q→Aut N	d	ρ	Label	ID
C₂₂.₁D₄ = C₈⋊D₁₁	φ: D₄/C₄ → C₂ ⊆ Aut C₂₂	88	2	C22.1D4	176,5
C₂₂.₂D₄ = D₈₈	φ: D₄/C₄ → C₂ ⊆ Aut C₂₂	88	2+	C22.2D4	176,6
C₂₂.₃D₄ = Dic₄₄	φ: D₄/C₄ → C₂ ⊆ Aut C₂₂	176	2-	C22.3D4	176,7
C₂₂.₄D₄ = C₄₄⋊C₄	φ: D₄/C₄ → C₂ ⊆ Aut C₂₂	176		C22.4D4	176,12
C₂₂.₅D₄ = Dic₁₁⋊C₄	φ: D₄/C₂² → C₂ ⊆ Aut C₂₂	176		C22.5D4	176,11
C₂₂.₆D₄ = D₂₂⋊C₄	φ: D₄/C₂² → C₂ ⊆ Aut C₂₂	88		C22.6D4	176,13
C₂₂.₇D₄ = D₄⋊D₁₁	φ: D₄/C₂² → C₂ ⊆ Aut C₂₂	88	4+	C22.7D4	176,14
C₂₂.₈D₄ = D₄.D₁₁	φ: D₄/C₂² → C₂ ⊆ Aut C₂₂	88	4-	C22.8D4	176,15
C₂₂.₉D₄ = Q₈⋊D₁₁	φ: D₄/C₂² → C₂ ⊆ Aut C₂₂	88	4+	C22.9D4	176,16
C₂₂.₁₀D₄ = C₁₁⋊Q₁₆	φ: D₄/C₂² → C₂ ⊆ Aut C₂₂	176	4-	C22.10D4	176,17
C₂₂.₁₁D₄ = C₂³.D₁₁	φ: D₄/C₂² → C₂ ⊆ Aut C₂₂	88		C22.11D4	176,18
C₂₂.₁₂D₄ = C₁₁×C₂²⋊C₄	central extension (φ=1)	88		C22.12D4	176,20
C₂₂.₁₃D₄ = C₁₁×C₄⋊C₄	central extension (φ=1)	176		C22.13D4	176,21
C₂₂.₁₄D₄ = C₁₁×D₈	central extension (φ=1)	88	2	C22.14D4	176,24
C₂₂.₁₅D₄ = C₁₁×SD₁₆	central extension (φ=1)	88	2	C22.15D4	176,25
C₂₂.₁₆D₄ = C₁₁×Q₁₆	central extension (φ=1)	176	2	C22.16D4	176,26

׿

×

⋊

ℤ

𝔽

○

≀

ℚ

◁