Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
764 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 764 conjugacy classes of subgroups — too many to draw. Only its 141 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. C22×#14523514 | C2 | semidirect |
| 2. C2×#16862267 | C2 | semidirect |
| 3. #22553822 | C2 | semidirect |
| 4. #22553477 | C2 | semidirect |
| 5. #22553468 | C2 | semidirect |
| 6. #22553465 | C2 | semidirect |
| 7. #22553456 | C2 | semidirect |
| 8. #22553445 | C2 | semidirect |
| 9. #22553307 | C2 | semidirect |
| 10. C22⋊C8×D131 | C2 | semidirect |
| 11. #448×C131 | C2 | semidirect |
| 17. C2×#14523512 | C22 | semidirect |
| 23. C2×#14523503 | C22 | semidirect |
| 24. C2×#14523502 | C22 | semidirect |
| 25. C2×#14523498 | C22 | semidirect |
| 26. C2×C8×D131 | C22 | semidirect |
| 28. #16862226 | C22 | semidirect |
| 30. #16862217 | C22 | semidirect |
| 34. #16862204 | C22 | semidirect |
| 35. #16862170 | C22 | semidirect |
| 36. #16862168 | C22 | semidirect |
| 37. #16862166 | C22 | semidirect |
| 39. (C2×D131)⋊C8 | C22 | semidirect |
| 41. C2×SD16×C131 | C22 | semidirect |
| 43. #103×C131 | C22 | semidirect |
| 52. #14523514 | D4 | semidirect |
| 146. C22×C131 | #135 | semidirect |
| 175. C131 | #3002 | semidirect |
| 184. #448 | D131 | semidirect |
| 202. C2×SD16 | C2×D131 | semidirect |
| 215. #103 | C2×D131 | semidirect |
| 333. C22 | #16862267 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14523514 | 2 |
| C2×#16862267 | 2 |
| #22553822 | 2 |
| #22553477 | 2 |
| #22553468 | 2 |
| #22553465 | 2 |
| #22553456 | 2 |
| #22553445 | 2 |
| #22553307 | 2 |
| C22⋊C8×D131 | 2 |
| #448×C131 | 2 |
| #3002 | 131 |