Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
548 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 548 conjugacy classes of subgroups — too many to draw. Only its 135 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×#22576185 | C2 | semidirect |
| 2. C2×M16×D271 | C2 | semidirect |
| 3. #31774404 | C2 | semidirect |
| 4. C2×#22576135 | C2 | semidirect |
| 5. #31774149 | C2 | semidirect |
| 6. #31774146 | C2 | semidirect |
| 7. #31774132 | C2 | semidirect |
| 8. #31774129 | C2 | semidirect |
| 9. #31773937 | C2 | semidirect |
| 10. #31773903 | C2 | semidirect |
| 11. #417×C271 | C2 | semidirect |
| 16. C2×#16864641 | C22 | semidirect |
| 17. C2×#16864639 | C22 | semidirect |
| 19. C2×#16864637 | C22 | semidirect |
| 21. C2×C8×D271 | C22 | semidirect |
| 23. #22576136 | C22 | semidirect |
| 24. #22576136 | C22 | semidirect |
| 29. #22576131 | C22 | semidirect |
| 30. #22576131 | C22 | semidirect |
| 36. #22576093 | C22 | semidirect |
| 37. #22576091 | C22 | semidirect |
| 38. #22576082 | C22 | semidirect |
| 39. #22576082 | C22 | semidirect |
| 43. #103×C271 | C22 | semidirect |
| 44. #102×C271 | C22 | semidirect |
| 65. #16864638 | D4 | semidirect |
| 120. C271⋊C8 | C2×D4 | semidirect |
| 154. C2×D271 | AGL(1,ℤ/8) | semidirect |
| 172. C271 | #3055 | semidirect |
| 184. #417 | D271 | semidirect |
| 214. #103 | C2×D271 | semidirect |
| 217. #102 | C2×D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22576185 | 2 |
| C2×M16×D271 | 2 |
| #31774404 | 2 |
| C2×#22576135 | 2 |
| #31774149 | 2 |
| #31774146 | 2 |
| #31774132 | 2 |
| #31774129 | 2 |
| #31773937 | 2 |
| #31773903 | 2 |
| #417×C271 | 2 |
| #3055 | 271 |