Extensions 1→N→G→Q→1 with N=C₄₂ and Q=C₂²

Direct product G=N×Q with N=C₄₂ and Q=C₂²

		d	ρ	Label	ID
C₂²×C₄₂		168		C2^2xC42	168,57

Semidirect products G=N:Q with N=C₄₂ and Q=C₂²

extension	φ:Q→Aut N	d	ρ	Label	ID
C₄₂⋊C₂² = C₂×S₃×D₇	φ: C₂²/C₁ → C₂² ⊆ Aut C₄₂	42	4+	C42:C2^2	168,50
C₄₂⋊₂C₂² = C₂²×D₂₁	φ: C₂²/C₂ → C₂ ⊆ Aut C₄₂	84		C42:2C2^2	168,56
C₄₂⋊₃C₂² = C₂×C₆×D₇	φ: C₂²/C₂ → C₂ ⊆ Aut C₄₂	84		C42:3C2^2	168,54
C₄₂⋊₄C₂² = S₃×C₂×C₁₄	φ: C₂²/C₂ → C₂ ⊆ Aut C₄₂	84		C42:4C2^2	168,55

Non-split extensions G=N.Q with N=C₄₂ and Q=C₂²

extension	φ:Q→Aut N	d	ρ	Label	ID
C₄₂.₁C₂² = Dic₃×D₇	φ: C₂²/C₁ → C₂² ⊆ Aut C₄₂	84	4-	C42.1C2^2	168,12
C₄₂.₂C₂² = S₃×Dic₇	φ: C₂²/C₁ → C₂² ⊆ Aut C₄₂	84	4-	C42.2C2^2	168,13
C₄₂.₃C₂² = D₂₁⋊C₄	φ: C₂²/C₁ → C₂² ⊆ Aut C₄₂	84	4+	C42.3C2^2	168,14
C₄₂.₄C₂² = C₂₁⋊D₄	φ: C₂²/C₁ → C₂² ⊆ Aut C₄₂	84	4-	C42.4C2^2	168,15
C₄₂.₅C₂² = C₃⋊D₂₈	φ: C₂²/C₁ → C₂² ⊆ Aut C₄₂	84	4+	C42.5C2^2	168,16
C₄₂.₆C₂² = C₇⋊D₁₂	φ: C₂²/C₁ → C₂² ⊆ Aut C₄₂	84	4+	C42.6C2^2	168,17
C₄₂.₇C₂² = C₂₁⋊Q₈	φ: C₂²/C₁ → C₂² ⊆ Aut C₄₂	168	4-	C42.7C2^2	168,18
C₄₂.₈C₂² = Dic₄₂	φ: C₂²/C₂ → C₂ ⊆ Aut C₄₂	168	2-	C42.8C2^2	168,34
C₄₂.₉C₂² = C₄×D₂₁	φ: C₂²/C₂ → C₂ ⊆ Aut C₄₂	84	2	C42.9C2^2	168,35
C₄₂.₁₀C₂² = D₈₄	φ: C₂²/C₂ → C₂ ⊆ Aut C₄₂	84	2+	C42.10C2^2	168,36
C₄₂.₁₁C₂² = C₂×Dic₂₁	φ: C₂²/C₂ → C₂ ⊆ Aut C₄₂	168		C42.11C2^2	168,37
C₄₂.₁₂C₂² = C₂₁⋊₇D₄	φ: C₂²/C₂ → C₂ ⊆ Aut C₄₂	84	2	C42.12C2^2	168,38
C₄₂.₁₃C₂² = C₃×Dic₁₄	φ: C₂²/C₂ → C₂ ⊆ Aut C₄₂	168	2	C42.13C2^2	168,24
C₄₂.₁₄C₂² = C₁₂×D₇	φ: C₂²/C₂ → C₂ ⊆ Aut C₄₂	84	2	C42.14C2^2	168,25
C₄₂.₁₅C₂² = C₃×D₂₈	φ: C₂²/C₂ → C₂ ⊆ Aut C₄₂	84	2	C42.15C2^2	168,26
C₄₂.₁₆C₂² = C₆×Dic₇	φ: C₂²/C₂ → C₂ ⊆ Aut C₄₂	168		C42.16C2^2	168,27
C₄₂.₁₇C₂² = C₃×C₇⋊D₄	φ: C₂²/C₂ → C₂ ⊆ Aut C₄₂	84	2	C42.17C2^2	168,28
C₄₂.₁₈C₂² = C₇×Dic₆	φ: C₂²/C₂ → C₂ ⊆ Aut C₄₂	168	2	C42.18C2^2	168,29
C₄₂.₁₉C₂² = S₃×C₂₈	φ: C₂²/C₂ → C₂ ⊆ Aut C₄₂	84	2	C42.19C2^2	168,30
C₄₂.₂₀C₂² = C₇×D₁₂	φ: C₂²/C₂ → C₂ ⊆ Aut C₄₂	84	2	C42.20C2^2	168,31
C₄₂.₂₁C₂² = Dic₃×C₁₄	φ: C₂²/C₂ → C₂ ⊆ Aut C₄₂	168		C42.21C2^2	168,32
C₄₂.₂₂C₂² = C₇×C₃⋊D₄	φ: C₂²/C₂ → C₂ ⊆ Aut C₄₂	84	2	C42.22C2^2	168,33
C₄₂.₂₃C₂² = D₄×C₂₁	central extension (φ=1)	84	2	C42.23C2^2	168,40
C₄₂.₂₄C₂² = Q₈×C₂₁	central extension (φ=1)	168	2	C42.24C2^2	168,41

⋊

ℤ

𝔽

○

≀

ℚ

◁

Extensions 1→N→G→Q→1 with N=C42 and Q=C22

Extensions 1→N→G→Q→1 with N=C₄₂ and Q=C₂²