# Extensions 1→N→G→Q→1 with N=C24 and Q=Q8

Direct product G=N×Q with N=C24 and Q=Q8
dρLabelID
Q8×C24128Q8xC2^4128,2321

Semidirect products G=N:Q with N=C24 and Q=Q8
extensionφ:Q→Aut NdρLabelID
C24⋊Q8 = C24⋊Q8φ: Q8/C1Q8 ⊆ Aut C24168+C2^4:Q8128,764
C242Q8 = C242Q8φ: Q8/C2C22 ⊆ Aut C2416C2^4:2Q8128,761
C243Q8 = C2×C23⋊Q8φ: Q8/C2C22 ⊆ Aut C2464C2^4:3Q8128,1117
C244Q8 = C244Q8φ: Q8/C2C22 ⊆ Aut C2432C2^4:4Q8128,1169
C245Q8 = C245Q8φ: Q8/C2C22 ⊆ Aut C2432C2^4:5Q8128,1358
C246Q8 = C246Q8φ: Q8/C2C22 ⊆ Aut C2432C2^4:6Q8128,1572
C247Q8 = C2×C232Q8φ: Q8/C2C22 ⊆ Aut C2432C2^4:7Q8128,2188
C248Q8 = C248Q8φ: Q8/C4C2 ⊆ Aut C2432C2^4:8Q8128,1580
C249Q8 = C22×C22⋊Q8φ: Q8/C4C2 ⊆ Aut C2464C2^4:9Q8128,2165

Non-split extensions G=N.Q with N=C24 and Q=Q8
extensionφ:Q→Aut NdρLabelID
C24.Q8 = C24.Q8φ: Q8/C1Q8 ⊆ Aut C24168+C2^4.Q8128,801
C24.2Q8 = C24.2Q8φ: Q8/C2C22 ⊆ Aut C2432C2^4.2Q8128,25
C24.3Q8 = C24.3Q8φ: Q8/C2C22 ⊆ Aut C2432C2^4.3Q8128,30
C24.4Q8 = C24.4Q8φ: Q8/C2C22 ⊆ Aut C2416C2^4.4Q8128,36
C24.5Q8 = C24.5Q8φ: Q8/C2C22 ⊆ Aut C2464C2^4.5Q8128,171
C24.6Q8 = C2×C4.10C42φ: Q8/C2C22 ⊆ Aut C2432C2^4.6Q8128,463
C24.7Q8 = C24.7Q8φ: Q8/C2C22 ⊆ Aut C2432C2^4.7Q8128,470
C24.8Q8 = C2×C23.9D4φ: Q8/C2C22 ⊆ Aut C2432C2^4.8Q8128,471
C24.9Q8 = C24.9Q8φ: Q8/C2C22 ⊆ Aut C2432C2^4.9Q8128,543
C24.10Q8 = C24.10Q8φ: Q8/C2C22 ⊆ Aut C2432C2^4.10Q8128,587
C24.11Q8 = C24.11Q8φ: Q8/C2C22 ⊆ Aut C24164C2^4.11Q8128,823
C24.12Q8 = C24.91D4φ: Q8/C2C22 ⊆ Aut C2432C2^4.12Q8128,1047
C24.13Q8 = C2×C23.Q8φ: Q8/C2C22 ⊆ Aut C2464C2^4.13Q8128,1121
C24.14Q8 = C2×C23.4Q8φ: Q8/C2C22 ⊆ Aut C2464C2^4.14Q8128,1125
C24.15Q8 = C24.15Q8φ: Q8/C2C22 ⊆ Aut C2432C2^4.15Q8128,1574
C24.16Q8 = C2×M4(2).C4φ: Q8/C2C22 ⊆ Aut C2432C2^4.16Q8128,1647
C24.17Q8 = C24.17Q8φ: Q8/C4C2 ⊆ Aut C2464C2^4.17Q8128,165
C24.18Q8 = C2×C4.C42φ: Q8/C4C2 ⊆ Aut C2464C2^4.18Q8128,469
C24.19Q8 = C24.19Q8φ: Q8/C4C2 ⊆ Aut C2432C2^4.19Q8128,542
C24.20Q8 = C2×C23.7Q8φ: Q8/C4C2 ⊆ Aut C2464C2^4.20Q8128,1010
C24.21Q8 = C2×C23.8Q8φ: Q8/C4C2 ⊆ Aut C2464C2^4.21Q8128,1018
C24.22Q8 = C22×C8.C4φ: Q8/C4C2 ⊆ Aut C2464C2^4.22Q8128,1646
C24.23Q8 = C22×C2.C42central extension (φ=1)128C2^4.23Q8128,998
C24.24Q8 = C23×C4⋊C4central extension (φ=1)128C2^4.24Q8128,2152

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