Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
760 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 760 conjugacy classes of subgroups — too many to draw. Only its 165 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. C2×D8×D131 | C2 | semidirect |
| 2. #127×D131 | C2 | semidirect |
| 3. #22553689 | C2 | semidirect |
| 4. #22553688 | C2 | semidirect |
| 5. #22553687 | C2 | semidirect |
| 6. C4×C8×D131 | C2 | semidirect |
| 7. #493×C131 | C2 | semidirect |
| 10. C2×D1048 | C22 | semidirect |
| 11. C2×#14523498 | C22 | semidirect |
| 14. #16862243 | C22 | semidirect |
| 16. #16862242 | C22 | semidirect |
| 18. C4×C131⋊C8 | C22 | semidirect |
| 19. C8×Dic131 | C22 | semidirect |
| 20. C2×D8×C131 | C22 | semidirect |
| 21. #127×C131 | C22 | semidirect |
| 22. C4×C8×C131 | C22 | semidirect |
| 35. C8×D131 | D4 | semidirect |
| 53. C4×D131 | D8 | semidirect |
| 55. C131⋊C8 | C2×D4 | semidirect |
| 61. C8×C131 | C2×D4 | semidirect |
| 70. C4×C131 | C2×D8 | semidirect |
| 73. Dic131 | C2×D8 | semidirect |
| 78. D131 | #493 | direct (N × H) |
| 79. C131 | C2×#493 | semidirect |
| 86. #493 | D131 | direct (N × H) |
| 93. C2×D8 | C2×D131 | semidirect |
| 98. #127 | C2×D131 | semidirect |
| 102. C4×C8 | C2×D131 | semidirect |
| 141. C8 | D4×D131 | semidirect |
| 152. C4 | D8×D131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D8×D131 | 2 |
| #127×D131 | 2 |
| #22553689 | 2 |
| #22553688 | 2 |
| #22553687 | 2 |
| C4×C8×D131 | 2 |
| #493×C131 | 2 |
| C2×#493 | 131 |