Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
176 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 176 conjugacy classes of subgroups — too many to draw. Only its 51 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. #22553660 | C2 | semidirect |
| 3. #22553390 | C2 | semidirect |
| 4. #22553062 | C2 | semidirect |
| 5. #22553058 | C2 | semidirect |
| 6. #22553055 | C2 | semidirect |
| 7. #461×C131 | C2 | semidirect |
| 84. C131 | #1701 | semidirect |
| 87. #461 | D131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22553660 | 2 |
| #22553507 | 2 |
| #22553390 | 2 |
| #22553062 | 2 |
| #22553058 | 2 |
| #22553055 | 2 |
| #461×C131 | 2 |
| #1701 | 131 |