Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
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×D131 | C2 | semidirect |
| 2. C2×#16862254 | C2 | semidirect |
| 3. #22553878 | C2 | semidirect |
| 4. #22553566 | C2 | semidirect |
| 5. #22553565 | C2 | semidirect |
| 6. #22553562 | C2 | semidirect |
| 7. #22553547 | C2 | semidirect |
| 8. #22553546 | C2 | semidirect |
| 9. #22553347 | C2 | semidirect |
| 10. #22553315 | C2 | semidirect |
| 11. #469×C131 | C2 | semidirect |
| 19. C2×#14523496 | C22 | semidirect |
| 20. C22×C131⋊C8 | C22 | semidirect |
| 22. C2×C8×D131 | C22 | semidirect |
| 25. #16862221 | C22 | semidirect |
| 26. #16862220 | C22 | semidirect |
| 27. #16862217 | C22 | semidirect |
| 31. #16862179 | C22 | semidirect |
| 32. #16862178 | C22 | semidirect |
| 33. #16862168 | C22 | semidirect |
| 34. #16862167 | C22 | semidirect |
| 35. #16862166 | C22 | semidirect |
| 37. C2×M16×C131 | C22 | semidirect |
| 38. #121×C131 | C22 | semidirect |
| 39. #106×C131 | C22 | semidirect |
| 40. #102×C131 | C22 | semidirect |
| 65. C8×D131 | D4 | semidirect |
| 146. C131 | #3058 | semidirect |
| 154. #469 | D131 | semidirect |
| 168. C2×M16 | C2×D131 | semidirect |
| 177. #121 | C2×D131 | semidirect |
| 183. #106 | C2×D131 | semidirect |
| 187. #102 | C2×D131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D8×D131 | 2 |
| C2×#16862254 | 2 |
| #22553878 | 2 |
| #22553566 | 2 |
| #22553565 | 2 |
| #22553562 | 2 |
| #22553547 | 2 |
| #22553546 | 2 |
| #22553347 | 2 |
| #22553315 | 2 |
| #469×C131 | 2 |
| #3058 | 131 |