Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
372 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 117 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 |
|---|---|---|
| 1. #22554036 | C2 | semidirect |
| 2. D4×Dic262 | C2 | semidirect |
| 3. #22553673 | C2 | semidirect |
| 4. #22553662 | C2 | semidirect |
| 5. #22553605 | C2 | semidirect |
| 6. #22553593 | C2 | semidirect |
| 8. #22553439 | C2 | semidirect |
| 9. #22553413 | C2 | semidirect |
| 11. #461×C131 | C2 | semidirect |
| 122. C131 | #3367 | semidirect |
| 131. #461 | D131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22554036 | 2 |
| D4×Dic262 | 2 |
| #22553673 | 2 |
| #22553662 | 2 |
| #22553605 | 2 |
| #22553593 | 2 |
| #22553529 | 2 |
| #22553439 | 2 |
| #22553413 | 2 |
| C4×#14523498 | 2 |
| #461×C131 | 2 |
| #3367 | 131 |