Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
704 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 704 conjugacy classes of subgroups — too many to draw. Only its 145 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. C2×#16862279 | C2 | semidirect |
| 3. #22553883 | C2 | semidirect |
| 4. #22553497 | C2 | semidirect |
| 5. #22553492 | C2 | semidirect |
| 6. #22553328 | C2 | semidirect |
| 7. #413×C131 | C2 | semidirect |
| 16. C22×Dic262 | C22 | semidirect |
| 18. #16862279 | C22 | semidirect |
| 21. #16862244 | C22 | semidirect |
| 22. #16862233 | C22 | semidirect |
| 25. #16862205 | C22 | semidirect |
| 26. #16862172 | C22 | semidirect |
| 28. C2×M16×C131 | C22 | semidirect |
| 29. #101×C131 | C22 | semidirect |
| 30. #100×C131 | C22 | semidirect |
| 129. C131 | #3022 | semidirect |
| 137. #413 | D131 | semidirect |
| 152. C2×M16 | C2×D131 | semidirect |
| 159. #101 | C2×D131 | semidirect |
| 160. #100 | C2×D131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22554148 | 2 |
| C2×#16862279 | 2 |
| #22553883 | 2 |
| #22553497 | 2 |
| #22553492 | 2 |
| #22553328 | 2 |
| #413×C131 | 2 |
| #3022 | 131 |