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

Direct product G=N×Q with N=C78 and Q=C22
dρLabelID
C22×C78312C2^2xC78312,61

Semidirect products G=N:Q with N=C78 and Q=C22
extensionφ:Q→Aut NdρLabelID
C78⋊C22 = C2×S3×D13φ: C22/C1C22 ⊆ Aut C78784+C78:C2^2312,54
C782C22 = C22×D39φ: C22/C2C2 ⊆ Aut C78156C78:2C2^2312,60
C783C22 = C2×C6×D13φ: C22/C2C2 ⊆ Aut C78156C78:3C2^2312,58
C784C22 = S3×C2×C26φ: C22/C2C2 ⊆ Aut C78156C78:4C2^2312,59

Non-split extensions G=N.Q with N=C78 and Q=C22
extensionφ:Q→Aut NdρLabelID
C78.1C22 = Dic3×D13φ: C22/C1C22 ⊆ Aut C781564-C78.1C2^2312,15
C78.2C22 = S3×Dic13φ: C22/C1C22 ⊆ Aut C781564-C78.2C2^2312,16
C78.3C22 = D78.C2φ: C22/C1C22 ⊆ Aut C781564+C78.3C2^2312,17
C78.4C22 = C39⋊D4φ: C22/C1C22 ⊆ Aut C781564-C78.4C2^2312,18
C78.5C22 = C3⋊D52φ: C22/C1C22 ⊆ Aut C781564+C78.5C2^2312,19
C78.6C22 = C13⋊D12φ: C22/C1C22 ⊆ Aut C781564+C78.6C2^2312,20
C78.7C22 = C39⋊Q8φ: C22/C1C22 ⊆ Aut C783124-C78.7C2^2312,21
C78.8C22 = Dic78φ: C22/C2C2 ⊆ Aut C783122-C78.8C2^2312,37
C78.9C22 = C4×D39φ: C22/C2C2 ⊆ Aut C781562C78.9C2^2312,38
C78.10C22 = D156φ: C22/C2C2 ⊆ Aut C781562+C78.10C2^2312,39
C78.11C22 = C2×Dic39φ: C22/C2C2 ⊆ Aut C78312C78.11C2^2312,40
C78.12C22 = C397D4φ: C22/C2C2 ⊆ Aut C781562C78.12C2^2312,41
C78.13C22 = C3×Dic26φ: C22/C2C2 ⊆ Aut C783122C78.13C2^2312,27
C78.14C22 = C12×D13φ: C22/C2C2 ⊆ Aut C781562C78.14C2^2312,28
C78.15C22 = C3×D52φ: C22/C2C2 ⊆ Aut C781562C78.15C2^2312,29
C78.16C22 = C6×Dic13φ: C22/C2C2 ⊆ Aut C78312C78.16C2^2312,30
C78.17C22 = C3×C13⋊D4φ: C22/C2C2 ⊆ Aut C781562C78.17C2^2312,31
C78.18C22 = C13×Dic6φ: C22/C2C2 ⊆ Aut C783122C78.18C2^2312,32
C78.19C22 = S3×C52φ: C22/C2C2 ⊆ Aut C781562C78.19C2^2312,33
C78.20C22 = C13×D12φ: C22/C2C2 ⊆ Aut C781562C78.20C2^2312,34
C78.21C22 = Dic3×C26φ: C22/C2C2 ⊆ Aut C78312C78.21C2^2312,35
C78.22C22 = C13×C3⋊D4φ: C22/C2C2 ⊆ Aut C781562C78.22C2^2312,36
C78.23C22 = D4×C39central extension (φ=1)1562C78.23C2^2312,43
C78.24C22 = Q8×C39central extension (φ=1)3122C78.24C2^2312,44

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