Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
492 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 129 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×D4×Dic131 | C2 | semidirect |
| 3. #22553626 | C2 | semidirect |
| 4. #22553623 | C2 | semidirect |
| 5. #22553590 | C2 | semidirect |
| 6. #22553505 | C2 | semidirect |
| 7. #22553446 | C2 | semidirect |
| 8. D8×Dic131 | C2 | semidirect |
| 9. #22553392 | C2 | semidirect |
| 10. #22553362 | C2 | semidirect |
| 11. #447×C131 | C2 | semidirect |
| 15. #16862245 | C22 | semidirect |
| 16. #16862242 | C22 | semidirect |
| 24. D4×Dic131 | C22 | semidirect |
| 25. #16862208 | C22 | semidirect |
| 30. #16862180 | C22 | semidirect |
| 31. #16862179 | C22 | semidirect |
| 32. Dic131⋊C8 | C22 | semidirect |
| 33. #16862168 | C22 | semidirect |
| 35. #16862167 | C22 | semidirect |
| 37. C8×Dic131 | C22 | semidirect |
| 96. C2×Dic131 | D8 | semidirect |
| 113. D4×C131 | #41 | semidirect |
| 149. C131 | #3100 | semidirect |
| 158. #447 | D131 | semidirect |
| 249. D4 | #14523512 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22553857 | 2 |
| C2×D4×Dic131 | 2 |
| #22553626 | 2 |
| #22553623 | 2 |
| #22553590 | 2 |
| #22553505 | 2 |
| #22553446 | 2 |
| D8×Dic131 | 2 |
| #22553392 | 2 |
| #22553362 | 2 |
| #447×C131 | 2 |
| #3100 | 131 |