Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
1412 conjugacy classes of subgroups; only the 545 normal subgroups are shown.
This group has 1412 conjugacy classes of subgroups — too many to draw. Only its 545 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. #22554148 | C2 | semidirect |
| 2. #22554127 | C2 | semidirect |
| 3. #22554120 | C2 | semidirect |
| 4. #22554110 | C2 | semidirect |
| 5. C2×#16862277 | C2 | semidirect |
| 6. #22554079 | C2 | semidirect |
| 7. C2×2−1+4×C131 | C2 | semidirect |
| 9. #16862293 | C22 | semidirect |
| 10. #16862292 | C22 | semidirect |
| 14. #16862277 | C22 | semidirect |
| 15. #16862277 | C22 | semidirect |
| 16. #16862276 | C22 | semidirect |
| 17. #16862272 | C22 | semidirect |
| 18. #16862271 | C22 | semidirect |
| 19. #16862266 | C22 | semidirect |
| 20. C2×#14523503 | C22 | semidirect |
| 21. C2×#14523500 | C22 | semidirect |
| 22. #16862253 | C22 | semidirect |
| 23. C2×#14523497 | C22 | semidirect |
| 25. 2−1+4×C131 | C22 | semidirect |
| 28. C2×#41×C131 | C22 | semidirect |
| 30. C22×Q8×C131 | C22 | semidirect |
| 112. C131 | #3586 | semidirect |
| 115. C2×2−1+4 | D131 | semidirect |
| 124. 2−1+4 | C2×D131 | semidirect |
| 131. C2×#41 | C2×D131 | semidirect |
| 133. C22×Q8 | C2×D131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22554148 | 2 |
| #22554127 | 2 |
| #22554120 | 2 |
| #22554110 | 2 |
| C2×#16862277 | 2 |
| #22554079 | 2 |
| C2×2−1+4×C131 | 2 |
| #3586 | 131 |