Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
490 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 490 conjugacy classes of subgroups — too many to draw. Only its 133 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×#16862276 | C2 | semidirect |
| 2. C22×#14523502 | C2 | semidirect |
| 4. #22553789 | C2 | semidirect |
| 5. #22553537 | C2 | semidirect |
| 6. #22553511 | C2 | semidirect |
| 7. #22553338 | C2 | semidirect |
| 8. #22553316 | C2 | semidirect |
| 9. #416×C131 | C2 | semidirect |
| 13. C2×#14523503 | C22 | semidirect |
| 16. C2×#14523501 | C22 | semidirect |
| 23. #16862211 | C22 | semidirect |
| 26. Dic131⋊C8 | C22 | semidirect |
| 31. #103×C131 | C22 | semidirect |
| 32. #102×C131 | C22 | semidirect |
| 36. C2×Dic262 | D4 | semidirect |
| 116. C131 | #3043 | semidirect |
| 126. #416 | D131 | semidirect |
| 147. #103 | C2×D131 | semidirect |
| 149. #102 | C2×D131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16862276 | 2 |
| C22×#14523502 | 2 |
| #22553876 | 2 |
| #22553789 | 2 |
| #22553537 | 2 |
| #22553511 | 2 |
| #22553338 | 2 |
| #22553316 | 2 |
| #416×C131 | 2 |
| #3043 | 131 |