Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
504 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 504 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×#16862274 | C2 | semidirect |
| 2. #22553890 | C2 | semidirect |
| 3. #22553876 | C2 | semidirect |
| 4. #22553565 | C2 | semidirect |
| 5. #22553558 | C2 | semidirect |
| 6. #22553548 | C2 | semidirect |
| 7. #22553541 | C2 | semidirect |
| 8. #22553354 | C2 | semidirect |
| 9. #22553309 | C2 | semidirect |
| 10. C2×#16862168 | C2 | semidirect |
| 11. C2×#131×C131 | C2 | semidirect |
| 19. #16862225 | C22 | semidirect |
| 23. #16862220 | C22 | semidirect |
| 29. #16862180 | C22 | semidirect |
| 30. #16862178 | C22 | semidirect |
| 31. #16862171 | C22 | semidirect |
| 32. #16862171 | C22 | semidirect |
| 35. #16862168 | C22 | semidirect |
| 36. #16862168 | C22 | semidirect |
| 40. C2×M16×C131 | C22 | semidirect |
| 42. C22×C8×C131 | C22 | semidirect |
| 79. M16×C131 | D4 | semidirect |
| 151. C131 | #3062 | semidirect |
| 154. C2×#131 | D131 | semidirect |
| 172. C2×M16 | C2×D131 | semidirect |
| 174. C22×C8 | C2×D131 | semidirect |
| 220. M16 | C22⋊D131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16862274 | 2 |
| #22553890 | 2 |
| #22553876 | 2 |
| #22553565 | 2 |
| #22553558 | 2 |
| #22553548 | 2 |
| #22553541 | 2 |
| #22553354 | 2 |
| #22553309 | 2 |
| C2×#16862168 | 2 |
| C2×#131×C131 | 2 |
| #3062 | 131 |