Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
504 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 133 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×#16862274 | C2 | semidirect |
| 2. C2×#16862266 | C2 | semidirect |
| 3. #22553876 | C2 | semidirect |
| 4. #22553793 | C2 | semidirect |
| 5. #22553537 | C2 | semidirect |
| 6. #22553530 | C2 | semidirect |
| 7. #22553511 | C2 | semidirect |
| 8. #22553506 | C2 | semidirect |
| 9. #22553340 | C2 | semidirect |
| 10. C2×#16862166 | C2 | semidirect |
| 11. #417×C131 | C2 | semidirect |
| 16. C2×#14523503 | C22 | semidirect |
| 18. C2×#14523501 | C22 | semidirect |
| 19. C2×#14523500 | C22 | semidirect |
| 21. C2×#14523498 | C22 | semidirect |
| 28. #16862211 | C22 | semidirect |
| 29. #16862208 | C22 | semidirect |
| 34. Dic131⋊C8 | C22 | semidirect |
| 35. Dic131⋊C8 | C22 | semidirect |
| 41. #103×C131 | C22 | semidirect |
| 42. #102×C131 | C22 | semidirect |
| 45. #14523513 | D4 | semidirect |
| 154. C131 | #3045 | semidirect |
| 165. #417 | D131 | semidirect |
| 194. #103 | C2×D131 | semidirect |
| 197. #102 | C2×D131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16862274 | 2 |
| C2×#16862266 | 2 |
| #22553876 | 2 |
| #22553793 | 2 |
| #22553537 | 2 |
| #22553530 | 2 |
| #22553511 | 2 |
| #22553506 | 2 |
| #22553340 | 2 |
| C2×#16862166 | 2 |
| #417×C131 | 2 |
| #3045 | 131 |