Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
402 conjugacy classes of subgroups; only the 161 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 161 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. #22553389 | C2 | semidirect |
| 3. #22553385 | C2 | semidirect |
| 4. #22553377 | C2 | semidirect |
| 5. #22553365 | C2 | semidirect |
| 6. #22553277 | C2 | semidirect |
| 7. #432×C131 | C2 | semidirect |
| 92. C131 | #2981 | semidirect |
| 98. #432 | D131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22553862 | 2 |
| #22553389 | 2 |
| #22553385 | 2 |
| #22553377 | 2 |
| #22553365 | 2 |
| #22553277 | 2 |
| #432×C131 | 2 |
| #2981 | 131 |