Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
184 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 184 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 |
|---|---|---|
| 2. #22553513 | C2 | semidirect |
| 3. #22553509 | C2 | semidirect |
| 4. #22553439 | C2 | semidirect |
| 5. #22553062 | C2 | semidirect |
| 6. #22553055 | C2 | semidirect |
| 7. #331×C131 | C2 | semidirect |
| 55. C131⋊C8 | SD16 | semidirect |
| 86. C131 | #1688 | semidirect |
| 94. #331 | D131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22553688 | 2 |
| #22553513 | 2 |
| #22553509 | 2 |
| #22553439 | 2 |
| #22553062 | 2 |
| #22553055 | 2 |
| #331×C131 | 2 |
| #1688 | 131 |