Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
458 conjugacy classes of subgroups; only the 177 normal subgroups are shown.
This group has 458 conjugacy classes of subgroups — too many to draw. Only its 177 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. #22554078 | C2 | semidirect |
| 3. #22553433 | C2 | semidirect |
| 4. #22553428 | C2 | semidirect |
| 5. C2×#16862172 | C2 | semidirect |
| 6. M16×Dic131 | C2 | semidirect |
| 7. #430×C131 | C2 | semidirect |
| 9. #16862279 | C4 | semidirect |
| 10. #16862274 | C4 | semidirect |
| 12. #16862254 | C22 | semidirect |
| 17. #16862172 | C22 | semidirect |
| 18. #16862172 | C22 | semidirect |
| 19. #16862156 | C22 | semidirect |
| 20. C8×Dic131 | C22 | semidirect |
| 23. #108×C131 | C22 | semidirect |
| 33. Dic524 | C2×C4 | semidirect |
| 34. #14523502 | C2×C4 | semidirect |
| 35. D1048 | C2×C4 | semidirect |
| 85. C131 | #2956 | semidirect |
| 91. #430 | D131 | semidirect |
| 105. #108 | C2×D131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22554112 | 2 |
| #22554078 | 2 |
| #22553433 | 2 |
| #22553428 | 2 |
| C2×#16862172 | 2 |
| M16×Dic131 | 2 |
| #430×C131 | 2 |
| #2956 | 131 |