Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
548 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 548 conjugacy classes of subgroups — too many to draw. Only its 135 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. C2×#16862274 | C2 | semidirect |
| 2. C2×#16862271 | C2 | semidirect |
| 3. #22553858 | C2 | semidirect |
| 4. C2×#16862208 | C2 | semidirect |
| 5. #22553530 | C2 | semidirect |
| 6. #22553526 | C2 | semidirect |
| 7. #22553516 | C2 | semidirect |
| 8. #22553506 | C2 | semidirect |
| 9. #22553335 | C2 | semidirect |
| 10. #22553311 | C2 | semidirect |
| 11. #417×C131 | C2 | semidirect |
| 22. #16862244 | C22 | semidirect |
| 23. #16862242 | C22 | semidirect |
| 24. #16862235 | C22 | semidirect |
| 25. #16862233 | C22 | semidirect |
| 36. Dic131⋊C8 | C22 | semidirect |
| 37. Dic131⋊C8 | C22 | semidirect |
| 38. #16862169 | C22 | semidirect |
| 39. #16862166 | C22 | semidirect |
| 43. #103×C131 | C22 | semidirect |
| 44. #102×C131 | C22 | semidirect |
| 51. C2×D524 | D4 | semidirect |
| 158. Dic131 | AGL(1,ℤ/8) | semidirect |
| 166. C131 | #3036 | semidirect |
| 178. #417 | D131 | semidirect |
| 209. #103 | C2×D131 | semidirect |
| 211. #102 | C2×D131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16862274 | 2 |
| C2×#16862271 | 2 |
| #22553858 | 2 |
| C2×#16862208 | 2 |
| #22553530 | 2 |
| #22553526 | 2 |
| #22553516 | 2 |
| #22553506 | 2 |
| #22553335 | 2 |
| #22553311 | 2 |
| #417×C131 | 2 |
| #3036 | 131 |