Extensions 1→N→G→Q→1 with N=C₂³.₃₁D₄ and Q=C₂

Direct product G=N×Q with N=C₂³.₃₁D₄ and Q=C₂

		d	ρ	Label	ID
C₂×C₂³.₃₁D₄		32		C2xC2^3.31D4	128,231

Semidirect products G=N:Q with N=C₂³.₃₁D₄ and Q=C₂

extension	φ:Q→Out N	d	Label	ID
C₂³.₃₁D₄⋊₁C₂ = C₂⁴.₅₉D₄	φ: C₂/C₁ → C₂ ⊆ Out C₂³.₃₁D₄	32	C2^3.31D4:1C2	128,248
C₂³.₃₁D₄⋊₂C₂ = C₂⁴.₆₁D₄	φ: C₂/C₁ → C₂ ⊆ Out C₂³.₃₁D₄	32	C2^3.31D4:2C2	128,252
C₂³.₃₁D₄⋊₃C₂ = C₄².₆₃D₄	φ: C₂/C₁ → C₂ ⊆ Out C₂³.₃₁D₄	32	C2^3.31D4:3C2	128,253
C₂³.₃₁D₄⋊₄C₂ = C₄⋊C₄.D₄	φ: C₂/C₁ → C₂ ⊆ Out C₂³.₃₁D₄	32	C2^3.31D4:4C2	128,329
C₂³.₃₁D₄⋊₅C₂ = C₂⁴.₉D₄	φ: C₂/C₁ → C₂ ⊆ Out C₂³.₃₁D₄	16	C2^3.31D4:5C2	128,332
C₂³.₃₁D₄⋊₆C₂ = C₂³⋊Q₁₆	φ: C₂/C₁ → C₂ ⊆ Out C₂³.₃₁D₄	32	C2^3.31D4:6C2	128,334
C₂³.₃₁D₄⋊₇C₂ = C₄⋊C₄.₁₂D₄	φ: C₂/C₁ → C₂ ⊆ Out C₂³.₃₁D₄	32	C2^3.31D4:7C2	128,341
C₂³.₃₁D₄⋊₈C₂ = C₂⁴.₁₅D₄	φ: C₂/C₁ → C₂ ⊆ Out C₂³.₃₁D₄	32	C2^3.31D4:8C2	128,344
C₂³.₃₁D₄⋊₉C₂ = C₂⁴.₁₇D₄	φ: C₂/C₁ → C₂ ⊆ Out C₂³.₃₁D₄	32	C2^3.31D4:9C2	128,346
C₂³.₃₁D₄⋊₁₀C₂ = C₂³⋊SD₁₆	φ: C₂/C₁ → C₂ ⊆ Out C₂³.₃₁D₄	16	C2^3.31D4:10C2	128,328
C₂³.₃₁D₄⋊₁₁C₂ = (C₂×C₄)⋊SD₁₆	φ: C₂/C₁ → C₂ ⊆ Out C₂³.₃₁D₄	32	C2^3.31D4:11C2	128,331
C₂³.₃₁D₄⋊₁₂C₂ = C₄⋊C₄.₆D₄	φ: C₂/C₁ → C₂ ⊆ Out C₂³.₃₁D₄	32	C2^3.31D4:12C2	128,335
C₂³.₃₁D₄⋊₁₃C₂ = C₂⁴.₁₂D₄	φ: C₂/C₁ → C₂ ⊆ Out C₂³.₃₁D₄	32	C2^3.31D4:13C2	128,338
C₂³.₃₁D₄⋊₁₄C₂ = C₂⁴.₁₄D₄	φ: C₂/C₁ → C₂ ⊆ Out C₂³.₃₁D₄	32	C2^3.31D4:14C2	128,340
C₂³.₃₁D₄⋊₁₅C₂ = C₄⋊C₄.₁₈D₄	φ: C₂/C₁ → C₂ ⊆ Out C₂³.₃₁D₄	32	C2^3.31D4:15C2	128,347
C₂³.₃₁D₄⋊₁₆C₂ = C₂⁴.₁₈D₄	φ: C₂/C₁ → C₂ ⊆ Out C₂³.₃₁D₄	32	C2^3.31D4:16C2	128,350
C₂³.₃₁D₄⋊₁₇C₂ = C₂⁴.₁₅₀D₄	φ: C₂/C₁ → C₂ ⊆ Out C₂³.₃₁D₄	16	C2^3.31D4:17C2	128,236
C₂³.₃₁D₄⋊₁₈C₂ = C₂⁴.₅₅D₄	φ: C₂/C₁ → C₂ ⊆ Out C₂³.₃₁D₄	32	C2^3.31D4:18C2	128,240
C₂³.₃₁D₄⋊₁₉C₂ = C₄².₅₇D₄	φ: C₂/C₁ → C₂ ⊆ Out C₂³.₃₁D₄	32	C2^3.31D4:19C2	128,241
C₂³.₃₁D₄⋊₂₀C₂ = C₂⁴.₅₇D₄	φ: C₂/C₁ → C₂ ⊆ Out C₂³.₃₁D₄	32	C2^3.31D4:20C2	128,243
C₂³.₃₁D₄⋊₂₁C₂ = C₄².₅₈D₄	φ: C₂/C₁ → C₂ ⊆ Out C₂³.₃₁D₄	32	C2^3.31D4:21C2	128,244
C₂³.₃₁D₄⋊₂₂C₂ = C₂⁴.₅₈D₄	φ: C₂/C₁ → C₂ ⊆ Out C₂³.₃₁D₄	32	C2^3.31D4:22C2	128,245
C₂³.₃₁D₄⋊₂₃C₂ = C₄².₃₇₅D₄	φ: trivial image	32	C2^3.31D4:23C2	128,232
C₂³.₃₁D₄⋊₂₄C₂ = C₂⁴.₅₃D₄	φ: trivial image	32	C2^3.31D4:24C2	128,233

Non-split extensions G=N.Q with N=C₂³.₃₁D₄ and Q=C₂

extension	φ:Q→Out N	d	Label	ID
C₂³.₃₁D₄.₁C₂ = C₄².₆₂D₄	φ: C₂/C₁ → C₂ ⊆ Out C₂³.₃₁D₄	32	C2^3.31D4.1C2	128,250
C₂³.₃₁D₄.₂C₂ = (C₂×C₄)⋊Q₁₆	φ: C₂/C₁ → C₂ ⊆ Out C₂³.₃₁D₄	32	C2^3.31D4.2C2	128,337
C₂³.₃₁D₄.₃C₂ = C₄⋊C₄.₂₀D₄	φ: C₂/C₁ → C₂ ⊆ Out C₂³.₃₁D₄	32	C2^3.31D4.3C2	128,349
C₂³.₃₁D₄.₄C₂ = (C₂×C₄).SD₁₆	φ: C₂/C₁ → C₂ ⊆ Out C₂³.₃₁D₄	32	C2^3.31D4.4C2	128,343
C₂³.₃₁D₄.₅C₂ = C₄².₅₆D₄	φ: C₂/C₁ → C₂ ⊆ Out C₂³.₃₁D₄	32	C2^3.31D4.5C2	128,238
C₂³.₃₁D₄.₆C₂ = C₄².₆₀D₄	φ: C₂/C₁ → C₂ ⊆ Out C₂³.₃₁D₄	32	C2^3.31D4.6C2	128,247
C₂³.₃₁D₄.₇C₂ = C₄².₄₀₄D₄	φ: trivial image	32	C2^3.31D4.7C2	128,235

⋊

ℤ

𝔽

○

≀

ℚ

◁

Extensions 1→N→G→Q→1 with N=C23.31D4 and Q=C2

Extensions 1→N→G→Q→1 with N=C₂³.₃₁D₄ and Q=C₂