Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
492 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 181 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 |
|---|---|---|
| 2. #22553790 | C2 | semidirect |
| 4. #22553415 | C2 | semidirect |
| 5. #22553397 | C2 | semidirect |
| 6. #22553348 | C2 | semidirect |
| 8. #22553270 | C2 | semidirect |
| 9. #419×C131 | C2 | semidirect |
| 11. C2×#14523500 | C4 | semidirect |
| 16. Q8×Dic131 | C22 | semidirect |
| 23. #16862179 | C22 | semidirect |
| 24. #16862177 | C22 | semidirect |
| 26. #16862156 | C22 | semidirect |
| 27. C8×Dic131 | C22 | semidirect |
| 31. #103×C131 | C22 | semidirect |
| 38. #14523500 | C2×C4 | semidirect |
| 39. #14523500 | C2×C4 | semidirect |
| 40. C2×C131⋊C8 | C2×C4 | semidirect |
| 54. C2×Q8×C131 | C2×C4 | semidirect |
| 103. C131 | #2949 | semidirect |
| 111. #419 | D131 | semidirect |
| 132. #103 | C2×D131 | semidirect |
| 139. C2×Q8 | C4×D131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14523500 | 2 |
| #22553790 | 2 |
| #22553786 | 2 |
| #22553415 | 2 |
| #22553397 | 2 |
| #22553348 | 2 |
| #22553318 | 2 |
| #22553270 | 2 |
| #419×C131 | 2 |
| #2949 | 131 |