Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
524 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 524 conjugacy classes of subgroups — too many to draw. Only its 127 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×D8×D271 | C2 | semidirect |
| 2. C2×#22576168 | C2 | semidirect |
| 3. #31774463 | C2 | semidirect |
| 4. #31774151 | C2 | semidirect |
| 5. #31774150 | C2 | semidirect |
| 6. #31774147 | C2 | semidirect |
| 7. #31774132 | C2 | semidirect |
| 8. #31774131 | C2 | semidirect |
| 9. #31773932 | C2 | semidirect |
| 10. #31773900 | C2 | semidirect |
| 11. #469×C271 | C2 | semidirect |
| 19. C2×#16864637 | C22 | semidirect |
| 20. C22×C271⋊C8 | C22 | semidirect |
| 22. C2×C8×D271 | C22 | semidirect |
| 25. #22576135 | C22 | semidirect |
| 26. #22576134 | C22 | semidirect |
| 27. #22576131 | C22 | semidirect |
| 31. #22576093 | C22 | semidirect |
| 32. #22576092 | C22 | semidirect |
| 33. #22576082 | C22 | semidirect |
| 34. #22576081 | C22 | semidirect |
| 35. #22576080 | C22 | semidirect |
| 37. C2×M16×C271 | C22 | semidirect |
| 38. #121×C271 | C22 | semidirect |
| 39. #106×C271 | C22 | semidirect |
| 40. #102×C271 | C22 | semidirect |
| 65. C8×D271 | D4 | semidirect |
| 146. C271 | #3058 | semidirect |
| 154. #469 | D271 | semidirect |
| 168. C2×M16 | C2×D271 | semidirect |
| 177. #121 | C2×D271 | semidirect |
| 183. #106 | C2×D271 | semidirect |
| 187. #102 | C2×D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D8×D271 | 2 |
| C2×#22576168 | 2 |
| #31774463 | 2 |
| #31774151 | 2 |
| #31774150 | 2 |
| #31774147 | 2 |
| #31774132 | 2 |
| #31774131 | 2 |
| #31773932 | 2 |
| #31773900 | 2 |
| #469×C271 | 2 |
| #3058 | 271 |