Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
242 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 242 conjugacy classes of subgroups — too many to draw. Only its 65 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. #22553368 | C2 | semidirect |
| 3. #22553364 | C2 | semidirect |
| 4. #22553058 | C2 | semidirect |
| 5. #22553055 | C2 | semidirect |
| 6. #22553055 | C2 | semidirect |
| 7. #332×C131 | C2 | semidirect |
| 96. C131 | #1553 | semidirect |
| 102. #332 | D131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22553863 | 2 |
| #22553368 | 2 |
| #22553364 | 2 |
| #22553058 | 2 |
| #22553055 | 2 |
| #332×C131 | 2 |
| #1553 | 131 |