Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
410 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 410 conjugacy classes of subgroups — too many to draw. Only its 137 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. #22553650 | C2 | semidirect |
| 3. #22553645 | C2 | semidirect |
| 4. #22553640 | C2 | semidirect |
| 5. #22553352 | C2 | semidirect |
| 6. #22553321 | C2 | semidirect |
| 18. #16862179 | C22 | semidirect |
| 19. #16862177 | C22 | semidirect |
| 20. #16862170 | C22 | semidirect |
| 21. #16862170 | C22 | semidirect |
| 116. C131 | #3095 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16862205 | 2 |
| #22553650 | 2 |
| #22553645 | 2 |
| #22553640 | 2 |
| #22553352 | 2 |
| #22553321 | 2 |
| #22553276 | 2 |
| C2×C22⋊Q8×C131 | 2 |
| #3095 | 131 |