Finite Group DatabasebetaFinite Group DatabasebetaOrder 10688.
428 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 428 conjugacy classes of subgroups — too many to draw. Only its 115 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 | D42 |
| 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. C22×D668 | C2 | semidirect |
| 2. C2×D4×D167 | C2 | semidirect |
| 3. C2×D4×D167 | C2 | semidirect |
| 4. #19128828 | C2 | semidirect |
| 5. #19128807 | C2 | semidirect |
| 6. #19128805 | C2 | semidirect |
| 7. #19128802 | C2 | semidirect |
| 8. #19128800 | C2 | semidirect |
| 9. #19128794 | C2 | semidirect |
| 10. C4×C22⋊D167 | C2 | semidirect |
| 11. #121×C167 | C2 | semidirect |
| 12. C23×D167 | C22 | semidirect |
| 13. C23×D167 | C22 | semidirect |
| 16. C2×D668 | C22 | semidirect |
| 17. C2×D668 | C22 | semidirect |
| 18. C2×D668 | C22 | semidirect |
| 20. C2×C22⋊D167 | C22 | semidirect |
| 21. C2×C22⋊D167 | C22 | semidirect |
| 22. C2×C22⋊D167 | C22 | semidirect |
| 25. C2×C4×D167 | C22 | semidirect |
| 26. C2×C4×D167 | C22 | semidirect |
| 27. Dic167⋊C4 | C22 | semidirect |
| 28. C22⋊Dic167 | C22 | semidirect |
| 29. (C2×D167)⋊C4 | C22 | semidirect |
| 30. (C2×D167)⋊C4 | C22 | semidirect |
| 31. (C2×D167)⋊C4 | C22 | semidirect |
| 32. C4×Dic167 | C22 | semidirect |
| 33. C2×D4×C167 | C22 | semidirect |
| 34. C2×D4×C167 | C22 | semidirect |
| 35. C22×C4×C167 | C22 | semidirect |
| 36. C4⋊C4×C167 | C22 | semidirect |
| 37. C22⋊C4×C167 | C22 | semidirect |
| 50. D668 | D4 | semidirect |
| 54. C22⋊D167 | D4 | semidirect |
| 73. C22×C167 | C2×D4 | semidirect |
| 84. C2×D167 | C2×D4 | semidirect |
| 85. C2×D167 | C2×D4 | semidirect |
| 88. C4×C167 | C2×D4 | semidirect |
| 91. Dic167 | C2×D4 | semidirect |
| 100. C167 | D42 | semidirect |
| 108. #121 | D167 | semidirect |
| 126. C2×D4 | C2×D167 | semidirect |
| 127. C2×D4 | C2×D167 | semidirect |
| 130. C22×C4 | C2×D167 | semidirect |
| 132. C4⋊C4 | C2×D167 | semidirect |
| 137. C22⋊C4 | C2×D167 | semidirect |
| 185. C22 | D4×D167 | semidirect |
| 192. C4 | D4×D167 | semidirect |