Extensions 1→N→G→Q→1 with N=C₂³ and Q=C₂²

Direct product G=N×Q with N=C₂³ and Q=C₂²

		d	ρ	Label	ID
C₂⁵		32		C2^5	32,51

Semidirect products G=N:Q with N=C₂³ and Q=C₂²

extension	φ:Q→Aut N	d	ρ	Label	ID
C₂³⋊₁C₂² = C₂²≀C₂	φ: C₂²/C₁ → C₂² ⊆ Aut C₂³	8		C2^3:1C2^2	32,27
C₂³⋊₂C₂² = 2₊¹⁺⁴	φ: C₂²/C₁ → C₂² ⊆ Aut C₂³	8	4+	C2^3:2C2^2	32,49
C₂³⋊₃C₂² = C₂²×D₄	φ: C₂²/C₂ → C₂ ⊆ Aut C₂³	16		C2^3:3C2^2	32,46

Non-split extensions G=N.Q with N=C₂³ and Q=C₂²

extension	φ:Q→Aut N	d	ρ	Label	ID
C₂³.₁C₂² = C₂³⋊C₄	φ: C₂²/C₁ → C₂² ⊆ Aut C₂³	8	4+	C2^3.1C2^2	32,6
C₂³.₂C₂² = C₄⋊D₄	φ: C₂²/C₁ → C₂² ⊆ Aut C₂³	16		C2^3.2C2^2	32,28
C₂³.₃C₂² = C₄.₄D₄	φ: C₂²/C₁ → C₂² ⊆ Aut C₂³	16		C2^3.3C2^2	32,31
C₂³.₄C₂² = C₄²⋊₂C₂	φ: C₂²/C₁ → C₂² ⊆ Aut C₂³	16		C2^3.4C2^2	32,33
C₂³.₅C₂² = C₄⋊₁D₄	φ: C₂²/C₁ → C₂² ⊆ Aut C₂³	16		C2^3.5C2^2	32,34
C₂³.₆C₂² = C₂×C₂²⋊C₄	φ: C₂²/C₂ → C₂ ⊆ Aut C₂³	16		C2^3.6C2^2	32,22
C₂³.₇C₂² = C₄²⋊C₂	φ: C₂²/C₂ → C₂ ⊆ Aut C₂³	16		C2^3.7C2^2	32,24
C₂³.₈C₂² = C₄×D₄	φ: C₂²/C₂ → C₂ ⊆ Aut C₂³	16		C2^3.8C2^2	32,25
C₂³.₉C₂² = C₂²⋊Q₈	φ: C₂²/C₂ → C₂ ⊆ Aut C₂³	16		C2^3.9C2^2	32,29
C₂³.₁₀C₂² = C₂².D₄	φ: C₂²/C₂ → C₂ ⊆ Aut C₂³	16		C2^3.10C2^2	32,30
C₂³.₁₁C₂² = C₂×C₄○D₄	φ: C₂²/C₂ → C₂ ⊆ Aut C₂³	16		C2^3.11C2^2	32,48
C₂³.₁₂C₂² = C₂.C₄²	central extension (φ=1)	32		C2^3.12C2^2	32,2
C₂³.₁₃C₂² = C₂×C₄⋊C₄	central extension (φ=1)	32		C2^3.13C2^2	32,23
C₂³.₁₄C₂² = C₂²×Q₈	central extension (φ=1)	32		C2^3.14C2^2	32,47

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