Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
376 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 376 conjugacy classes of subgroups — too many to draw. Only its 141 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. #22553616 | C2 | semidirect |
| 3. #22553609 | C2 | semidirect |
| 4. #22553604 | C2 | semidirect |
| 5. #22553589 | C2 | semidirect |
| 6. #22553355 | C2 | semidirect |
| 7. C2×#16862179 | C2 | semidirect |
| 8. #22553339 | C2 | semidirect |
| 11. #544×C131 | C2 | semidirect |
| 42. #14523513 | Q8 | semidirect |
| 123. C131 | #3083 | semidirect |
| 125. #544 | D131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22553792 | 2 |
| #22553616 | 2 |
| #22553609 | 2 |
| #22553604 | 2 |
| #22553589 | 2 |
| #22553355 | 2 |
| C2×#16862179 | 2 |
| #22553339 | 2 |
| #22553311 | 2 |
| #22553306 | 2 |
| #544×C131 | 2 |
| #3083 | 131 |