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Extensions 1→N→G→Q→1 with N=C68 and Q=C22

Direct product G=N×Q with N=C68 and Q=C22
dρLabelID
C22×C68272C2^2xC68272,46

Semidirect products G=N:Q with N=C68 and Q=C22
extensionφ:Q→Aut NdρLabelID
C68⋊C22 = D4×D17φ: C22/C1 → C22 ⊆ Aut C68684+C68:C2^2272,40
C68⋊2C22 = C2×D68φ: C22/C2 → C2 ⊆ Aut C68136C68:2C2^2272,38
C68⋊3C22 = C2×C4×D17φ: C22/C2 → C2 ⊆ Aut C68136C68:3C2^2272,37
C68⋊4C22 = D4×C34φ: C22/C2 → C2 ⊆ Aut C68136C68:4C2^2272,47

Non-split extensions G=N.Q with N=C68 and Q=C22
extensionφ:Q→Aut NdρLabelID
C68.1C22 = D4⋊D17φ: C22/C1 → C22 ⊆ Aut C681364+C68.1C2^2272,15
C68.2C22 = D4.D17φ: C22/C1 → C22 ⊆ Aut C681364-C68.2C2^2272,16
C68.3C22 = Q8⋊D17φ: C22/C1 → C22 ⊆ Aut C681364+C68.3C2^2272,17
C68.4C22 = C17⋊Q16φ: C22/C1 → C22 ⊆ Aut C682724-C68.4C2^2272,18
C68.5C22 = D4⋊2D17φ: C22/C1 → C22 ⊆ Aut C681364-C68.5C2^2272,41
C68.6C22 = Q8×D17φ: C22/C1 → C22 ⊆ Aut C681364-C68.6C2^2272,42
C68.7C22 = D68⋊C2φ: C22/C1 → C22 ⊆ Aut C681364+C68.7C2^2272,43
C68.8C22 = C136⋊C2φ: C22/C2 → C2 ⊆ Aut C681362C68.8C2^2272,6
C68.9C22 = D136φ: C22/C2 → C2 ⊆ Aut C681362+C68.9C2^2272,7
C68.10C22 = Dic68φ: C22/C2 → C2 ⊆ Aut C682722-C68.10C2^2272,8
C68.11C22 = C2×Dic34φ: C22/C2 → C2 ⊆ Aut C68272C68.11C2^2272,36
C68.12C22 = C8×D17φ: C22/C2 → C2 ⊆ Aut C681362C68.12C2^2272,4
C68.13C22 = C8⋊D17φ: C22/C2 → C2 ⊆ Aut C681362C68.13C2^2272,5
C68.14C22 = C2×C17⋊3C8φ: C22/C2 → C2 ⊆ Aut C68272C68.14C2^2272,9
C68.15C22 = C68.4C4φ: C22/C2 → C2 ⊆ Aut C681362C68.15C2^2272,10
C68.16C22 = D68⋊5C2φ: C22/C2 → C2 ⊆ Aut C681362C68.16C2^2272,39
C68.17C22 = D8×C17φ: C22/C2 → C2 ⊆ Aut C681362C68.17C2^2272,25
C68.18C22 = SD16×C17φ: C22/C2 → C2 ⊆ Aut C681362C68.18C2^2272,26
C68.19C22 = Q16×C17φ: C22/C2 → C2 ⊆ Aut C682722C68.19C2^2272,27
C68.20C22 = Q8×C34φ: C22/C2 → C2 ⊆ Aut C68272C68.20C2^2272,48
C68.21C22 = C4○D4×C17φ: C22/C2 → C2 ⊆ Aut C681362C68.21C2^2272,49
C68.22C22 = M4(2)×C17central extension (φ=1)1362C68.22C2^2272,24

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