Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
596 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 596 conjugacy classes of subgroups — too many to draw. Only its 149 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×#16862268 | C2 | semidirect |
| 3. #22553879 | C2 | semidirect |
| 4. #22553700 | C2 | semidirect |
| 5. #22553695 | C2 | semidirect |
| 6. #22553687 | C2 | semidirect |
| 7. #22553267 | C2 | semidirect |
| 8. C22×D8×C131 | C2 | semidirect |
| 12. C2×Dic524 | C22 | semidirect |
| 13. C2×#14523502 | C22 | semidirect |
| 14. C2×#14523501 | C22 | semidirect |
| 15. C2×D1048 | C22 | semidirect |
| 16. C2×#14523498 | C22 | semidirect |
| 18. #16862242 | C22 | semidirect |
| 19. #16862233 | C22 | semidirect |
| 23. #16862156 | C22 | semidirect |
| 24. C8×Dic131 | C22 | semidirect |
| 42. #14523497 | D4 | semidirect |
| 56. C2×C8×C131 | D4 | semidirect |
| 101. C131 | #3155 | semidirect |
| 105. C22×D8 | D131 | semidirect |
| 154. C2×C8 | C22⋊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×#16862268 | 2 |
| #22553879 | 2 |
| #22553700 | 2 |
| #22553695 | 2 |
| #22553687 | 2 |
| #22553267 | 2 |
| C22×D8×C131 | 2 |
| #3155 | 131 |