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×#16862272 | C2 | semidirect |
| 2. C2×#16862252 | C2 | semidirect |
| 3. #22553893 | C2 | semidirect |
| 4. #22553879 | C2 | semidirect |
| 5. #22553564 | C2 | semidirect |
| 6. #22553557 | C2 | semidirect |
| 7. #22553547 | C2 | semidirect |
| 8. #22553540 | C2 | semidirect |
| 9. #22553352 | C2 | semidirect |
| 10. #22553309 | C2 | semidirect |
| 11. C2×#102×C131 | C2 | semidirect |
| 19. C2×#14523496 | C22 | semidirect |
| 20. C2×C8×D131 | C22 | semidirect |
| 24. #16862226 | C22 | semidirect |
| 26. #16862221 | C22 | semidirect |
| 32. #16862179 | C22 | semidirect |
| 33. #16862177 | C22 | semidirect |
| 34. #16862171 | C22 | semidirect |
| 35. #16862171 | C22 | semidirect |
| 36. #16862168 | C22 | semidirect |
| 37. #16862168 | C22 | semidirect |
| 60. #14523497 | D4 | semidirect |
| 151. C131 | #3062 | semidirect |
| 163. C2×#102 | D131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16862272 | 2 |
| C2×#16862252 | 2 |
| #22553893 | 2 |
| #22553879 | 2 |
| #22553564 | 2 |
| #22553557 | 2 |
| #22553547 | 2 |
| #22553540 | 2 |
| #22553352 | 2 |
| #22553309 | 2 |
| C2×#102×C131 | 2 |
| #3062 | 131 |