# Extensions 1→N→G→Q→1 with N=C78 and Q=C6

Direct product G=N×Q with N=C78 and Q=C6
dρLabelID
C6×C78468C6xC78468,55

Semidirect products G=N:Q with N=C78 and Q=C6
extensionφ:Q→Aut NdρLabelID
C781C6 = C2×D39⋊C3φ: C6/C1C6 ⊆ Aut C78786+C78:1C6468,35
C782C6 = C6×C13⋊C6φ: C6/C1C6 ⊆ Aut C78786C78:2C6468,33
C783C6 = C2×S3×C13⋊C3φ: C6/C1C6 ⊆ Aut C78786C78:3C6468,34
C784C6 = C2×C6×C13⋊C3φ: C6/C2C3 ⊆ Aut C78156C78:4C6468,47
C785C6 = C6×D39φ: C6/C3C2 ⊆ Aut C781562C78:5C6468,52
C786C6 = C3×C6×D13φ: C6/C3C2 ⊆ Aut C78234C78:6C6468,50
C787C6 = S3×C78φ: C6/C3C2 ⊆ Aut C781562C78:7C6468,51

Non-split extensions G=N.Q with N=C78 and Q=C6
extensionφ:Q→Aut NdρLabelID
C78.1C6 = C393C12φ: C6/C1C6 ⊆ Aut C781566-C78.1C6468,21
C78.2C6 = C132C36φ: C6/C1C6 ⊆ Aut C784686C78.2C6468,1
C78.3C6 = C2×C13⋊C18φ: C6/C1C6 ⊆ Aut C782346C78.3C6468,8
C78.4C6 = C3×C26.C6φ: C6/C1C6 ⊆ Aut C781566C78.4C6468,19
C78.5C6 = Dic3×C13⋊C3φ: C6/C1C6 ⊆ Aut C781566C78.5C6468,20
C78.6C6 = C4×C13⋊C9φ: C6/C2C3 ⊆ Aut C784683C78.6C6468,2
C78.7C6 = C22×C13⋊C9φ: C6/C2C3 ⊆ Aut C78468C78.7C6468,12
C78.8C6 = C12×C13⋊C3φ: C6/C2C3 ⊆ Aut C781563C78.8C6468,22
C78.9C6 = C3×Dic39φ: C6/C3C2 ⊆ Aut C781562C78.9C6468,25
C78.10C6 = C9×Dic13φ: C6/C3C2 ⊆ Aut C784682C78.10C6468,4
C78.11C6 = C18×D13φ: C6/C3C2 ⊆ Aut C782342C78.11C6468,15
C78.12C6 = C32×Dic13φ: C6/C3C2 ⊆ Aut C78468C78.12C6468,23
C78.13C6 = Dic3×C39φ: C6/C3C2 ⊆ Aut C781562C78.13C6468,24

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