Extensions 1→N→G→Q→1 with N=C₄ and Q=D₃₄

Direct product G=N×Q with N=C₄ and Q=D₃₄

		d	ρ	Label	ID
C₂×C₄×D₁₇		136		C2xC4xD17	272,37

Semidirect products G=N:Q with N=C₄ and Q=D₃₄

extension	φ:Q→Aut N	d	ρ	Label	ID
C₄⋊₁D₃₄ = D₄×D₁₇	φ: D₃₄/D₁₇ → C₂ ⊆ Aut C₄	68	4+	C4:1D34	272,40
C₄⋊₂D₃₄ = C₂×D₆₈	φ: D₃₄/C₃₄ → C₂ ⊆ Aut C₄	136		C4:2D34	272,38

Non-split extensions G=N.Q with N=C₄ and Q=D₃₄

extension	φ:Q→Aut N	d	ρ	Label	ID
C₄.₁D₃₄ = D₄⋊D₁₇	φ: D₃₄/D₁₇ → C₂ ⊆ Aut C₄	136	4+	C4.1D34	272,15
C₄.₂D₃₄ = D₄.D₁₇	φ: D₃₄/D₁₇ → C₂ ⊆ Aut C₄	136	4-	C4.2D34	272,16
C₄.₃D₃₄ = Q₈⋊D₁₇	φ: D₃₄/D₁₇ → C₂ ⊆ Aut C₄	136	4+	C4.3D34	272,17
C₄.₄D₃₄ = C₁₇⋊Q₁₆	φ: D₃₄/D₁₇ → C₂ ⊆ Aut C₄	272	4-	C4.4D34	272,18
C₄.₅D₃₄ = D₄⋊₂D₁₇	φ: D₃₄/D₁₇ → C₂ ⊆ Aut C₄	136	4-	C4.5D34	272,41
C₄.₆D₃₄ = Q₈×D₁₇	φ: D₃₄/D₁₇ → C₂ ⊆ Aut C₄	136	4-	C4.6D34	272,42
C₄.₇D₃₄ = D₆₈⋊C₂	φ: D₃₄/D₁₇ → C₂ ⊆ Aut C₄	136	4+	C4.7D34	272,43
C₄.₈D₃₄ = C₁₃₆⋊C₂	φ: D₃₄/C₃₄ → C₂ ⊆ Aut C₄	136	2	C4.8D34	272,6
C₄.₉D₃₄ = D₁₃₆	φ: D₃₄/C₃₄ → C₂ ⊆ Aut C₄	136	2+	C4.9D34	272,7
C₄.₁₀D₃₄ = Dic₆₈	φ: D₃₄/C₃₄ → C₂ ⊆ Aut C₄	272	2-	C4.10D34	272,8
C₄.₁₁D₃₄ = C₂×Dic₃₄	φ: D₃₄/C₃₄ → C₂ ⊆ Aut C₄	272		C4.11D34	272,36
C₄.₁₂D₃₄ = C₈×D₁₇	central extension (φ=1)	136	2	C4.12D34	272,4
C₄.₁₃D₃₄ = C₈⋊D₁₇	central extension (φ=1)	136	2	C4.13D34	272,5
C₄.₁₄D₃₄ = C₂×C₁₇⋊₃C₈	central extension (φ=1)	272		C4.14D34	272,9
C₄.₁₅D₃₄ = C₆₈.₄C₄	central extension (φ=1)	136	2	C4.15D34	272,10
C₄.₁₆D₃₄ = D₆₈⋊₅C₂	central extension (φ=1)	136	2	C4.16D34	272,39

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