Finite Group DatabasebetaFinite Group DatabasebetaOrder 10688.
330 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 330 conjugacy classes of subgroups — too many to draw. Only its 109 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D167 |
| commutator, socle, cosocle | C22×C167 | C24 |
| Fitting | #121×C167 | C2 |
| hypercenter | #121 | D167 |
| hypocenter | C167 | #525 |
| LCS | G ▷ C22×C167 ▷ C167 | |
| UCS | C1 ◁ C22 ◁ #121 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#14581949 | C2 | semidirect |
| 2. C22×C4×D167 | C2 | semidirect |
| 3. #19128814 | C2 | semidirect |
| 4. #19128812 | C2 | semidirect |
| 5. #19128811 | C2 | semidirect |
| 6. #19128803 | C2 | semidirect |
| 7. #19128800 | C2 | semidirect |
| 8. D4×Dic167 | C2 | semidirect |
| 9. (C22⋊D167)⋊C4 | C2 | semidirect |
| 10. #19128790 | C2 | semidirect |
| 11. #121×C167 | C2 | semidirect |
| 14. C2×Dic334 | C22 | semidirect |
| 18. C22×Dic167 | C22 | semidirect |
| 24. C4⋊Dic167 | C22 | semidirect |
| 25. C4⋊Dic167 | C22 | semidirect |
| 26. Dic167⋊C4 | C22 | semidirect |
| 28. C22⋊Dic167 | C22 | semidirect |
| 31. C4×Dic167 | C22 | semidirect |
| 33. C2×D4×C167 | C22 | semidirect |
| 35. C4⋊C4×C167 | C22 | semidirect |
| 36. C22⋊C4×C167 | C22 | semidirect |
| 54. C4×D167 | D4 | semidirect |
| 68. C22×C167 | #41 | semidirect |
| 76. C2×D167 | #41 | semidirect |
| 91. C167 | #525 | semidirect |
| 99. #121 | D167 | semidirect |
| 110. C2×D4 | C2×D167 | semidirect |
| 122. C4⋊C4 | C2×D167 | semidirect |
| 127. C22⋊C4 | C2×D167 | semidirect |
| 167. C22 | #14581949 | semidirect |