Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
332 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 332 conjugacy classes of subgroups — too many to draw. Only its 79 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. #22554078 | C2 | semidirect |
| 3. #22553329 | C2 | semidirect |
| 4. #22553285 | C2 | semidirect |
| 5. #22553073 | C2 | semidirect |
| 6. #22553071 | C2 | semidirect |
| 7. #421×C131 | C2 | semidirect |
| 13. #16862244 | C4 | semidirect |
| 14. #16862242 | C4 | semidirect |
| 15. #16862235 | C4 | semidirect |
| 16. #16862233 | C4 | semidirect |
| 38. #14523497 | D4 | semidirect |
| 61. M16×C131 | D4 | semidirect |
| 125. C131 | #1884 | semidirect |
| 130. #421 | D131 | semidirect |
| 176. M16 | C22⋊D131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22554078 | 2 |
| #22553858 | 2 |
| #22553329 | 2 |
| #22553285 | 2 |
| #22553073 | 2 |
| #22553071 | 2 |
| #421×C131 | 2 |
| #1884 | 131 |