Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
732 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 732 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×#16862294 | C2 | semidirect |
| 2. C2×#16862274 | C2 | semidirect |
| 3. C22×#14523500 | C2 | semidirect |
| 4. #22553881 | C2 | semidirect |
| 5. #22553460 | C2 | semidirect |
| 6. #22553452 | C2 | semidirect |
| 7. #22553306 | C2 | semidirect |
| 8. #22553280 | C2 | semidirect |
| 9. #419×C131 | C2 | semidirect |
| 13. C2×#14523514 | C22 | semidirect |
| 18. C2×Q8×D131 | C22 | semidirect |
| 30. #16862169 | C22 | semidirect |
| 31. #16862166 | C22 | semidirect |
| 32. (C2×D131)⋊C8 | C22 | semidirect |
| 36. #103×C131 | C22 | semidirect |
| 45. #14523513 | D4 | semidirect |
| 74. C2×Q8×C131 | D4 | semidirect |
| 145. C131 | #3010 | semidirect |
| 153. #419 | D131 | semidirect |
| 180. #103 | C2×D131 | semidirect |
| 200. C2×Q8 | D524 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16862294 | 2 |
| C2×#16862274 | 2 |
| C22×#14523500 | 2 |
| #22553881 | 2 |
| #22553460 | 2 |
| #22553452 | 2 |
| #22553306 | 2 |
| #22553280 | 2 |
| #419×C131 | 2 |
| #3010 | 131 |