Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
494 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 494 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 |
|---|---|---|
| 2. C22×#14523502 | C2 | semidirect |
| 3. #22553883 | C2 | semidirect |
| 4. #22553786 | C2 | semidirect |
| 5. #22553526 | C2 | semidirect |
| 6. #22553516 | C2 | semidirect |
| 7. #22553338 | C2 | semidirect |
| 8. #22553320 | C2 | semidirect |
| 9. #416×C131 | C2 | semidirect |
| 18. #16862244 | C22 | semidirect |
| 19. #16862233 | C22 | semidirect |
| 26. Dic131⋊C8 | C22 | semidirect |
| 27. #16862169 | C22 | semidirect |
| 31. #103×C131 | C22 | semidirect |
| 32. #102×C131 | C22 | semidirect |
| 116. C131 | #3042 | semidirect |
| 126. #416 | D131 | semidirect |
| 148. #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×#16862271 | 2 |
| C22×#14523502 | 2 |
| #22553883 | 2 |
| #22553786 | 2 |
| #22553526 | 2 |
| #22553516 | 2 |
| #22553338 | 2 |
| #22553320 | 2 |
| #416×C131 | 2 |
| #3042 | 131 |