Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
256 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 73 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. #22553364 | C2 | semidirect |
| 3. C4⋊C8×D131 | C2 | semidirect |
| 4. #22553059 | C2 | semidirect |
| 5. #22553057 | C2 | semidirect |
| 6. #22553056 | C2 | semidirect |
| 7. #331×C131 | C2 | semidirect |
| 97. C131 | #1540 | semidirect |
| 105. #331 | D131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22553860 | 2 |
| #22553364 | 2 |
| C4⋊C8×D131 | 2 |
| #22553059 | 2 |
| #22553057 | 2 |
| #22553056 | 2 |
| #331×C131 | 2 |
| #1540 | 131 |