Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
492 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 125 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. #22553857 | C2 | semidirect |
| 2. C2×#16862208 | C2 | semidirect |
| 3. #22553625 | C2 | semidirect |
| 4. #22553591 | C2 | semidirect |
| 5. #22553506 | C2 | semidirect |
| 6. #22553448 | C2 | semidirect |
| 7. #22553445 | C2 | semidirect |
| 8. #22553394 | C2 | semidirect |
| 9. #22553392 | C2 | semidirect |
| 10. #22553362 | C2 | semidirect |
| 11. #480×C131 | C2 | semidirect |
| 17. #16862245 | C22 | semidirect |
| 18. #16862242 | C22 | semidirect |
| 22. D4×Dic131 | C22 | semidirect |
| 27. #16862208 | C22 | semidirect |
| 31. #16862179 | C22 | semidirect |
| 32. Dic131⋊C8 | C22 | semidirect |
| 35. #16862166 | C22 | semidirect |
| 37. C8×Dic131 | C22 | semidirect |
| 40. #107×C131 | C22 | semidirect |
| 41. #102×C131 | C22 | semidirect |
| 92. D524 | #41 | semidirect |
| 99. C2×Dic131 | D8 | semidirect |
| 149. C131 | #3100 | semidirect |
| 154. #480 | D131 | semidirect |
| 184. #107 | C2×D131 | semidirect |
| 189. #102 | C2×D131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22553857 | 2 |
| C2×#16862208 | 2 |
| #22553625 | 2 |
| #22553591 | 2 |
| #22553506 | 2 |
| #22553448 | 2 |
| #22553445 | 2 |
| #22553394 | 2 |
| #22553392 | 2 |
| #22553362 | 2 |
| #480×C131 | 2 |
| #3100 | 131 |