Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
466 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 466 conjugacy classes of subgroups — too many to draw. Only its 129 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. #22554110 | C2 | semidirect |
| 2. C2×#16862274 | C2 | semidirect |
| 3. C2×#16862271 | C2 | semidirect |
| 4. #22554078 | C2 | semidirect |
| 5. #22553581 | C2 | semidirect |
| 6. #22553578 | C2 | semidirect |
| 7. #22553360 | C2 | semidirect |
| 8. C2×#16862162 | C2 | semidirect |
| 9. #413×C131 | C2 | semidirect |
| 12. #16862277 | C22 | semidirect |
| 16. #16862272 | C22 | semidirect |
| 22. C2×#14523500 | C22 | semidirect |
| 24. C2×#14523498 | C22 | semidirect |
| 25. #16862254 | C22 | semidirect |
| 30. #16862181 | C22 | semidirect |
| 31. #16862162 | C22 | semidirect |
| 35. #101×C131 | C22 | semidirect |
| 36. #100×C131 | C22 | semidirect |
| 147. C131 | #3068 | semidirect |
| 156. #413 | D131 | semidirect |
| 182. #101 | C2×D131 | semidirect |
| 184. #100 | C2×D131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22554110 | 2 |
| C2×#16862274 | 2 |
| C2×#16862271 | 2 |
| #22554078 | 2 |
| #22553581 | 2 |
| #22553578 | 2 |
| #22553360 | 2 |
| C2×#16862162 | 2 |
| #413×C131 | 2 |
| #3068 | 131 |