Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
492 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 127 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. #22553860 | C2 | semidirect |
| 2. C4×D4×D131 | C2 | semidirect |
| 3. #22553624 | C2 | semidirect |
| 4. #22553593 | C2 | semidirect |
| 5. #22553592 | C2 | semidirect |
| 6. #22553504 | C2 | semidirect |
| 7. #22553444 | C2 | semidirect |
| 8. D8×Dic131 | C2 | semidirect |
| 9. #22553392 | C2 | semidirect |
| 10. #22553364 | C2 | semidirect |
| 11. #459×C131 | C2 | semidirect |
| 16. #16862246 | C22 | semidirect |
| 23. D4×Dic131 | C22 | semidirect |
| 30. #16862180 | C22 | semidirect |
| 31. #16862179 | C22 | semidirect |
| 32. C4⋊(C131⋊C8) | C22 | semidirect |
| 35. #16862167 | C22 | semidirect |
| 37. C8×Dic131 | C22 | semidirect |
| 39. #127×C131 | C22 | semidirect |
| 41. C4⋊C8×C131 | C22 | semidirect |
| 42. #102×C131 | C22 | semidirect |
| 91. D524 | #41 | semidirect |
| 107. C4×D131 | D8 | semidirect |
| 116. D4×C131 | #41 | semidirect |
| 154. C131 | #3100 | semidirect |
| 162. #459 | D131 | semidirect |
| 173. #127 | C2×D131 | semidirect |
| 191. C4⋊C8 | C2×D131 | semidirect |
| 195. #102 | C2×D131 | semidirect |
| 256. D4 | #14523512 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22553860 | 2 |
| C4×D4×D131 | 2 |
| #22553624 | 2 |
| #22553593 | 2 |
| #22553592 | 2 |
| #22553504 | 2 |
| #22553444 | 2 |
| D8×Dic131 | 2 |
| #22553392 | 2 |
| #22553364 | 2 |
| #459×C131 | 2 |
| #3100 | 131 |