Extensions 1→N→G→Q→1 with N=C₂⁴⋊₄S₃ and Q=C₂

Direct product G=N×Q with N=C₂⁴⋊₄S₃ and Q=C₂

		d	ρ	Label	ID
C₂×C₂⁴⋊₄S₃		48		C2xC2^4:4S3	192,1399

Semidirect products G=N:Q with N=C₂⁴⋊₄S₃ and Q=C₂

extension	φ:Q→Out N	d	ρ	Label	ID
C₂⁴⋊₄S₃⋊₁C₂ = C₂⁴⋊₆D₆	φ: C₂/C₁ → C₂ ⊆ Out C₂⁴⋊₄S₃	24	4	C2^4:4S3:1C2	192,591
C₂⁴⋊₄S₃⋊₂C₂ = C₂⁴.₃₈D₆	φ: C₂/C₁ → C₂ ⊆ Out C₂⁴⋊₄S₃	48		C2^4:4S3:2C2	192,1049
C₂⁴⋊₄S₃⋊₃C₂ = C₂⁴.₄₁D₆	φ: C₂/C₁ → C₂ ⊆ Out C₂⁴⋊₄S₃	48		C2^4:4S3:3C2	192,1053
C₂⁴⋊₄S₃⋊₄C₂ = C₂⁴.₆₇D₆	φ: C₂/C₁ → C₂ ⊆ Out C₂⁴⋊₄S₃	48		C2^4:4S3:4C2	192,1145
C₂⁴⋊₄S₃⋊₅C₂ = S₃×C₂²≀C₂	φ: C₂/C₁ → C₂ ⊆ Out C₂⁴⋊₄S₃	24		C2^4:4S3:5C2	192,1147
C₂⁴⋊₄S₃⋊₆C₂ = C₂⁴⋊₇D₆	φ: C₂/C₁ → C₂ ⊆ Out C₂⁴⋊₄S₃	48		C2^4:4S3:6C2	192,1148
C₂⁴⋊₄S₃⋊₇C₂ = C₂⁴.₄₅D₆	φ: C₂/C₁ → C₂ ⊆ Out C₂⁴⋊₄S₃	48		C2^4:4S3:7C2	192,1151
C₂⁴⋊₄S₃⋊₈C₂ = C₂⁴.₄₆D₆	φ: C₂/C₁ → C₂ ⊆ Out C₂⁴⋊₄S₃	48		C2^4:4S3:8C2	192,1152
C₂⁴⋊₄S₃⋊₉C₂ = C₂⁴⋊₉D₆	φ: C₂/C₁ → C₂ ⊆ Out C₂⁴⋊₄S₃	48		C2^4:4S3:9C2	192,1153
C₂⁴⋊₄S₃⋊₁₀C₂ = C₂⁴.₄₇D₆	φ: C₂/C₁ → C₂ ⊆ Out C₂⁴⋊₄S₃	48		C2^4:4S3:10C2	192,1154
C₂⁴⋊₄S₃⋊₁₁C₂ = D₄×C₃⋊D₄	φ: C₂/C₁ → C₂ ⊆ Out C₂⁴⋊₄S₃	48		C2^4:4S3:11C2	192,1360
C₂⁴⋊₄S₃⋊₁₂C₂ = C₂⁴⋊₁₂D₆	φ: C₂/C₁ → C₂ ⊆ Out C₂⁴⋊₄S₃	48		C2^4:4S3:12C2	192,1363
C₂⁴⋊₄S₃⋊₁₃C₂ = C₂⁴.₅₂D₆	φ: C₂/C₁ → C₂ ⊆ Out C₂⁴⋊₄S₃	48		C2^4:4S3:13C2	192,1364
C₂⁴⋊₄S₃⋊₁₄C₂ = C₂⁴.₅₃D₆	φ: C₂/C₁ → C₂ ⊆ Out C₂⁴⋊₄S₃	48		C2^4:4S3:14C2	192,1365
C₂⁴⋊₄S₃⋊₁₅C₂ = C₂⁴.₈₃D₆	φ: trivial image	48		C2^4:4S3:15C2	192,1350

Non-split extensions G=N.Q with N=C₂⁴⋊₄S₃ and Q=C₂

extension	φ:Q→Out N	d	ρ	Label	ID
C₂⁴⋊₄S₃.C₂ = C₂⁴.₄₂D₆	φ: C₂/C₁ → C₂ ⊆ Out C₂⁴⋊₄S₃	48		C2^4:4S3.C2	192,1054

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