Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
532 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 532 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×#16862277 | C2 | semidirect |
| 2. C2×#16862276 | C2 | semidirect |
| 4. C22×#14523503 | C2 | semidirect |
| 5. #22553888 | C2 | semidirect |
| 6. #22553707 | C2 | semidirect |
| 7. #22553704 | C2 | semidirect |
| 8. #22553694 | C2 | semidirect |
| 9. #22553691 | C2 | semidirect |
| 10. #22553268 | C2 | semidirect |
| 11. #536×C131 | C2 | semidirect |
| 143. C131 | #3156 | semidirect |
| 150. #536 | D131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16862277 | 2 |
| C2×#16862276 | 2 |
| C2×#16862266 | 2 |
| C22×#14523503 | 2 |
| #22553888 | 2 |
| #22553707 | 2 |
| #22553704 | 2 |
| #22553694 | 2 |
| #22553691 | 2 |
| #22553268 | 2 |
| #536×C131 | 2 |
| #3156 | 131 |