# Extensions 1→N→G→Q→1 with N=C7⋊C8 and Q=C22

Direct product G=N×Q with N=C7⋊C8 and Q=C22
dρLabelID
C22×C7⋊C8224C2^2xC7:C8224,115

Semidirect products G=N:Q with N=C7⋊C8 and Q=C22
extensionφ:Q→Out NdρLabelID
C7⋊C81C22 = D8⋊D7φ: C22/C1C22 ⊆ Out C7⋊C8564C7:C8:1C2^2224,106
C7⋊C82C22 = D56⋊C2φ: C22/C1C22 ⊆ Out C7⋊C8564+C7:C8:2C2^2224,109
C7⋊C83C22 = D4.D14φ: C22/C1C22 ⊆ Out C7⋊C8564C7:C8:3C2^2224,127
C7⋊C84C22 = D4⋊D14φ: C22/C1C22 ⊆ Out C7⋊C8564+C7:C8:4C2^2224,144
C7⋊C85C22 = D7×D8φ: C22/C2C2 ⊆ Out C7⋊C8564+C7:C8:5C2^2224,105
C7⋊C86C22 = D7×SD16φ: C22/C2C2 ⊆ Out C7⋊C8564C7:C8:6C2^2224,108
C7⋊C87C22 = C2×D4⋊D7φ: C22/C2C2 ⊆ Out C7⋊C8112C7:C8:7C2^2224,126
C7⋊C88C22 = C2×D4.D7φ: C22/C2C2 ⊆ Out C7⋊C8112C7:C8:8C2^2224,128
C7⋊C89C22 = C2×Q8⋊D7φ: C22/C2C2 ⊆ Out C7⋊C8112C7:C8:9C2^2224,136
C7⋊C810C22 = C2×C8⋊D7φ: C22/C2C2 ⊆ Out C7⋊C8112C7:C8:10C2^2224,95
C7⋊C811C22 = D7×M4(2)φ: C22/C2C2 ⊆ Out C7⋊C8564C7:C8:11C2^2224,101
C7⋊C812C22 = C2×C4.Dic7φ: C22/C2C2 ⊆ Out C7⋊C8112C7:C8:12C2^2224,116
C7⋊C813C22 = D7×C2×C8φ: trivial image112C7:C8:13C2^2224,94

Non-split extensions G=N.Q with N=C7⋊C8 and Q=C22
extensionφ:Q→Out NdρLabelID
C7⋊C8.1C22 = SD16⋊D7φ: C22/C1C22 ⊆ Out C7⋊C81124-C7:C8.1C2^2224,110
C7⋊C8.2C22 = Q16⋊D7φ: C22/C1C22 ⊆ Out C7⋊C81124C7:C8.2C2^2224,113
C7⋊C8.3C22 = C28.C23φ: C22/C1C22 ⊆ Out C7⋊C81124C7:C8.3C2^2224,137
C7⋊C8.4C22 = D4.9D14φ: C22/C1C22 ⊆ Out C7⋊C81124-C7:C8.4C2^2224,146
C7⋊C8.5C22 = D83D7φ: C22/C2C2 ⊆ Out C7⋊C81124-C7:C8.5C2^2224,107
C7⋊C8.6C22 = SD163D7φ: C22/C2C2 ⊆ Out C7⋊C81124C7:C8.6C2^2224,111
C7⋊C8.7C22 = D7×Q16φ: C22/C2C2 ⊆ Out C7⋊C81124-C7:C8.7C2^2224,112
C7⋊C8.8C22 = Q8.D14φ: C22/C2C2 ⊆ Out C7⋊C81124+C7:C8.8C2^2224,114
C7⋊C8.9C22 = C2×C7⋊Q16φ: C22/C2C2 ⊆ Out C7⋊C8224C7:C8.9C2^2224,138
C7⋊C8.10C22 = D4.8D14φ: C22/C2C2 ⊆ Out C7⋊C81124C7:C8.10C2^2224,145
C7⋊C8.11C22 = D28.2C4φ: C22/C2C2 ⊆ Out C7⋊C81122C7:C8.11C2^2224,96
C7⋊C8.12C22 = D28.C4φ: C22/C2C2 ⊆ Out C7⋊C81124C7:C8.12C2^2224,102
C7⋊C8.13C22 = Q8.Dic7φ: C22/C2C2 ⊆ Out C7⋊C81124C7:C8.13C2^2224,143

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