Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
596 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 596 conjugacy classes of subgroups — too many to draw. Only its 165 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×#16862268 | C2 | semidirect |
| 3. C22×D1048 | C2 | semidirect |
| 4. #22553881 | C2 | semidirect |
| 5. #22553701 | C2 | semidirect |
| 6. #22553696 | C2 | semidirect |
| 7. #22553689 | C2 | semidirect |
| 8. #405×C131 | C2 | semidirect |
| 13. C2×Dic524 | C22 | semidirect |
| 14. C2×#14523502 | C22 | semidirect |
| 15. C2×#14523502 | C22 | semidirect |
| 19. C2×D1048 | C22 | semidirect |
| 20. C2×D1048 | C22 | semidirect |
| 21. #16862243 | C22 | semidirect |
| 22. #16862234 | C22 | semidirect |
| 28. #97×C131 | C22 | semidirect |
| 29. C4×C8×C131 | C22 | semidirect |
| 51. M16×C131 | D4 | semidirect |
| 52. C2×C8×C131 | D4 | semidirect |
| 101. C131 | #3155 | semidirect |
| 110. #405 | D131 | semidirect |
| 130. #97 | C2×D131 | semidirect |
| 131. C4×C8 | C2×D131 | semidirect |
| 152. M16 | D524 | semidirect |
| 153. C2×C8 | D524 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16862274 | 2 |
| C2×#16862268 | 2 |
| C22×D1048 | 2 |
| #22553881 | 2 |
| #22553701 | 2 |
| #22553696 | 2 |
| #22553689 | 2 |
| #405×C131 | 2 |
| #3155 | 131 |