Extensions 1→N→G→Q→1 with N=C₇₈ and Q=C₂²

Direct product G=N×Q with N=C₇₈ and Q=C₂²

		d	ρ	Label	ID
C₂²×C₇₈		312		C2^2xC78	312,61

Semidirect products G=N:Q with N=C₇₈ and Q=C₂²

extension	φ:Q→Aut N	d	ρ	Label	ID
C₇₈⋊C₂² = C₂×S₃×D₁₃	φ: C₂²/C₁ → C₂² ⊆ Aut C₇₈	78	4+	C78:C2^2	312,54
C₇₈⋊₂C₂² = C₂²×D₃₉	φ: C₂²/C₂ → C₂ ⊆ Aut C₇₈	156		C78:2C2^2	312,60
C₇₈⋊₃C₂² = C₂×C₆×D₁₃	φ: C₂²/C₂ → C₂ ⊆ Aut C₇₈	156		C78:3C2^2	312,58
C₇₈⋊₄C₂² = S₃×C₂×C₂₆	φ: C₂²/C₂ → C₂ ⊆ Aut C₇₈	156		C78:4C2^2	312,59

Non-split extensions G=N.Q with N=C₇₈ and Q=C₂²

extension	φ:Q→Aut N	d	ρ	Label	ID
C₇₈.₁C₂² = Dic₃×D₁₃	φ: C₂²/C₁ → C₂² ⊆ Aut C₇₈	156	4-	C78.1C2^2	312,15
C₇₈.₂C₂² = S₃×Dic₁₃	φ: C₂²/C₁ → C₂² ⊆ Aut C₇₈	156	4-	C78.2C2^2	312,16
C₇₈.₃C₂² = D₇₈.C₂	φ: C₂²/C₁ → C₂² ⊆ Aut C₇₈	156	4+	C78.3C2^2	312,17
C₇₈.₄C₂² = C₃₉⋊D₄	φ: C₂²/C₁ → C₂² ⊆ Aut C₇₈	156	4-	C78.4C2^2	312,18
C₇₈.₅C₂² = C₃⋊D₅₂	φ: C₂²/C₁ → C₂² ⊆ Aut C₇₈	156	4+	C78.5C2^2	312,19
C₇₈.₆C₂² = C₁₃⋊D₁₂	φ: C₂²/C₁ → C₂² ⊆ Aut C₇₈	156	4+	C78.6C2^2	312,20
C₇₈.₇C₂² = C₃₉⋊Q₈	φ: C₂²/C₁ → C₂² ⊆ Aut C₇₈	312	4-	C78.7C2^2	312,21
C₇₈.₈C₂² = Dic₇₈	φ: C₂²/C₂ → C₂ ⊆ Aut C₇₈	312	2-	C78.8C2^2	312,37
C₇₈.₉C₂² = C₄×D₃₉	φ: C₂²/C₂ → C₂ ⊆ Aut C₇₈	156	2	C78.9C2^2	312,38
C₇₈.₁₀C₂² = D₁₅₆	φ: C₂²/C₂ → C₂ ⊆ Aut C₇₈	156	2+	C78.10C2^2	312,39
C₇₈.₁₁C₂² = C₂×Dic₃₉	φ: C₂²/C₂ → C₂ ⊆ Aut C₇₈	312		C78.11C2^2	312,40
C₇₈.₁₂C₂² = C₃₉⋊₇D₄	φ: C₂²/C₂ → C₂ ⊆ Aut C₇₈	156	2	C78.12C2^2	312,41
C₇₈.₁₃C₂² = C₃×Dic₂₆	φ: C₂²/C₂ → C₂ ⊆ Aut C₇₈	312	2	C78.13C2^2	312,27
C₇₈.₁₄C₂² = C₁₂×D₁₃	φ: C₂²/C₂ → C₂ ⊆ Aut C₇₈	156	2	C78.14C2^2	312,28
C₇₈.₁₅C₂² = C₃×D₅₂	φ: C₂²/C₂ → C₂ ⊆ Aut C₇₈	156	2	C78.15C2^2	312,29
C₇₈.₁₆C₂² = C₆×Dic₁₃	φ: C₂²/C₂ → C₂ ⊆ Aut C₇₈	312		C78.16C2^2	312,30
C₇₈.₁₇C₂² = C₃×C₁₃⋊D₄	φ: C₂²/C₂ → C₂ ⊆ Aut C₇₈	156	2	C78.17C2^2	312,31
C₇₈.₁₈C₂² = C₁₃×Dic₆	φ: C₂²/C₂ → C₂ ⊆ Aut C₇₈	312	2	C78.18C2^2	312,32
C₇₈.₁₉C₂² = S₃×C₅₂	φ: C₂²/C₂ → C₂ ⊆ Aut C₇₈	156	2	C78.19C2^2	312,33
C₇₈.₂₀C₂² = C₁₃×D₁₂	φ: C₂²/C₂ → C₂ ⊆ Aut C₇₈	156	2	C78.20C2^2	312,34
C₇₈.₂₁C₂² = Dic₃×C₂₆	φ: C₂²/C₂ → C₂ ⊆ Aut C₇₈	312		C78.21C2^2	312,35
C₇₈.₂₂C₂² = C₁₃×C₃⋊D₄	φ: C₂²/C₂ → C₂ ⊆ Aut C₇₈	156	2	C78.22C2^2	312,36
C₇₈.₂₃C₂² = D₄×C₃₉	central extension (φ=1)	156	2	C78.23C2^2	312,43
C₇₈.₂₄C₂² = Q₈×C₃₉	central extension (φ=1)	312	2	C78.24C2^2	312,44

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Extensions 1→N→G→Q→1 with N=C78 and Q=C22

Extensions 1→N→G→Q→1 with N=C₇₈ and Q=C₂²