# Extensions 1→N→G→Q→1 with N=C72 and Q=C22

Direct product G=N×Q with N=C72 and Q=C22
dρLabelID
C22×C72288C2^2xC72288,179

Semidirect products G=N:Q with N=C72 and Q=C22
extensionφ:Q→Aut NdρLabelID
C721C22 = C8⋊D18φ: C22/C1C22 ⊆ Aut C72724+C72:1C2^2288,118
C722C22 = D8×D9φ: C22/C1C22 ⊆ Aut C72724+C72:2C2^2288,120
C723C22 = D72⋊C2φ: C22/C1C22 ⊆ Aut C72724+C72:3C2^2288,124
C724C22 = D8⋊D9φ: C22/C1C22 ⊆ Aut C72724C72:4C2^2288,121
C725C22 = SD16×D9φ: C22/C1C22 ⊆ Aut C72724C72:5C2^2288,123
C726C22 = M4(2)×D9φ: C22/C1C22 ⊆ Aut C72724C72:6C2^2288,116
C727C22 = C9×C8⋊C22φ: C22/C1C22 ⊆ Aut C72724C72:7C2^2288,186
C728C22 = C2×D72φ: C22/C2C2 ⊆ Aut C72144C72:8C2^2288,114
C729C22 = C2×C72⋊C2φ: C22/C2C2 ⊆ Aut C72144C72:9C2^2288,113
C7210C22 = C2×C8×D9φ: C22/C2C2 ⊆ Aut C72144C72:10C2^2288,110
C7211C22 = C2×C8⋊D9φ: C22/C2C2 ⊆ Aut C72144C72:11C2^2288,111
C7212C22 = D8×C18φ: C22/C2C2 ⊆ Aut C72144C72:12C2^2288,182
C7213C22 = SD16×C18φ: C22/C2C2 ⊆ Aut C72144C72:13C2^2288,183
C7214C22 = M4(2)×C18φ: C22/C2C2 ⊆ Aut C72144C72:14C2^2288,180

Non-split extensions G=N.Q with N=C72 and Q=C22
extensionφ:Q→Aut NdρLabelID
C72.1C22 = C8.D18φ: C22/C1C22 ⊆ Aut C721444-C72.1C2^2288,119
C72.2C22 = C9⋊D16φ: C22/C1C22 ⊆ Aut C721444+C72.2C2^2288,33
C72.3C22 = D8.D9φ: C22/C1C22 ⊆ Aut C721444-C72.3C2^2288,34
C72.4C22 = C9⋊SD32φ: C22/C1C22 ⊆ Aut C721444+C72.4C2^2288,35
C72.5C22 = C9⋊Q32φ: C22/C1C22 ⊆ Aut C722884-C72.5C2^2288,36
C72.6C22 = D83D9φ: C22/C1C22 ⊆ Aut C721444-C72.6C2^2288,122
C72.7C22 = Q16×D9φ: C22/C1C22 ⊆ Aut C721444-C72.7C2^2288,127
C72.8C22 = D725C2φ: C22/C1C22 ⊆ Aut C721444+C72.8C2^2288,129
C72.9C22 = SD16⋊D9φ: C22/C1C22 ⊆ Aut C721444-C72.9C2^2288,125
C72.10C22 = Q16⋊D9φ: C22/C1C22 ⊆ Aut C721444C72.10C2^2288,128
C72.11C22 = SD163D9φ: C22/C1C22 ⊆ Aut C721444C72.11C2^2288,126
C72.12C22 = D36.C4φ: C22/C1C22 ⊆ Aut C721444C72.12C2^2288,117
C72.13C22 = C9×C8.C22φ: C22/C1C22 ⊆ Aut C721444C72.13C2^2288,187
C72.14C22 = D144φ: C22/C2C2 ⊆ Aut C721442+C72.14C2^2288,6
C72.15C22 = C144⋊C2φ: C22/C2C2 ⊆ Aut C721442C72.15C2^2288,7
C72.16C22 = Dic72φ: C22/C2C2 ⊆ Aut C722882-C72.16C2^2288,8
C72.17C22 = C2×Dic36φ: C22/C2C2 ⊆ Aut C72288C72.17C2^2288,109
C72.18C22 = D727C2φ: C22/C2C2 ⊆ Aut C721442C72.18C2^2288,115
C72.19C22 = C16×D9φ: C22/C2C2 ⊆ Aut C721442C72.19C2^2288,4
C72.20C22 = C16⋊D9φ: C22/C2C2 ⊆ Aut C721442C72.20C2^2288,5
C72.21C22 = C2×C9⋊C16φ: C22/C2C2 ⊆ Aut C72288C72.21C2^2288,18
C72.22C22 = C36.C8φ: C22/C2C2 ⊆ Aut C721442C72.22C2^2288,19
C72.23C22 = D36.2C4φ: C22/C2C2 ⊆ Aut C721442C72.23C2^2288,112
C72.24C22 = C9×D16φ: C22/C2C2 ⊆ Aut C721442C72.24C2^2288,61
C72.25C22 = C9×SD32φ: C22/C2C2 ⊆ Aut C721442C72.25C2^2288,62
C72.26C22 = C9×Q32φ: C22/C2C2 ⊆ Aut C722882C72.26C2^2288,63
C72.27C22 = Q16×C18φ: C22/C2C2 ⊆ Aut C72288C72.27C2^2288,184
C72.28C22 = C9×C4○D8φ: C22/C2C2 ⊆ Aut C721442C72.28C2^2288,185
C72.29C22 = C9×M5(2)central extension (φ=1)1442C72.29C2^2288,60
C72.30C22 = C9×C8○D4central extension (φ=1)1442C72.30C2^2288,181

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