Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
700 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 700 conjugacy classes of subgroups — too many to draw. Only its 165 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. #22553240 | C2 | semidirect |
| 3. #22553185 | C2 | semidirect |
| 4. #22553184 | C2 | semidirect |
| 5. #22553175 | C2 | semidirect |
| 6. #22553173 | C2 | semidirect |
| 11. C2×Dic131⋊C4 | C22 | semidirect |
| 18. C131⋊#95 | C22 | semidirect |
| 19. C131⋊#95 | C22 | semidirect |
| 20. C131⋊#95 | C22 | semidirect |
| 116. C131 | #2483 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C22⋊Dic131 | 2 |
| #22553240 | 2 |
| #22553185 | 2 |
| #22553184 | 2 |
| #22553175 | 2 |
| #22553173 | 2 |
| #22553168 | 2 |
| C22×C22⋊C4×C131 | 2 |
| #2483 | 131 |