Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
348 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 115 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. #22554037 | C2 | semidirect |
| 3. #22553668 | C2 | semidirect |
| 5. #22553611 | C2 | semidirect |
| 6. #22553537 | C2 | semidirect |
| 8. #22553436 | C2 | semidirect |
| 9. C4×#14523503 | C2 | semidirect |
| 10. #22553399 | C2 | semidirect |
| 11. #475×C131 | C2 | semidirect |
| 117. C131 | #3365 | semidirect |
| 124. #475 | D131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22554047 | 2 |
| #22554037 | 2 |
| #22553668 | 2 |
| #22553660 | 2 |
| #22553611 | 2 |
| #22553537 | 2 |
| #22553513 | 2 |
| #22553436 | 2 |
| C4×#14523503 | 2 |
| #22553399 | 2 |
| #475×C131 | 2 |
| #3365 | 131 |