Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
528 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 528 conjugacy classes of subgroups — too many to draw. Only its 181 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. #22553786 | C2 | semidirect |
| 3. #22553423 | C2 | semidirect |
| 4. #22553394 | C2 | semidirect |
| 5. #22553316 | C2 | semidirect |
| 6. #22553267 | C2 | semidirect |
| 7. #427×C131 | C2 | semidirect |
| 9. C2×D1048 | C4 | semidirect |
| 14. #16862208 | C22 | semidirect |
| 17. #16862166 | C22 | semidirect |
| 18. #16862156 | C22 | semidirect |
| 19. C8×Dic131 | C22 | semidirect |
| 22. #107×C131 | C22 | semidirect |
| 23. #106×C131 | C22 | semidirect |
| 27. C2×D524 | C2×C4 | semidirect |
| 30. D1048 | C2×C4 | semidirect |
| 31. D1048 | C2×C4 | semidirect |
| 39. C2×C8×C131 | C2×C4 | semidirect |
| 77. C131 | #2948 | semidirect |
| 83. #427 | D131 | semidirect |
| 97. #107 | C2×D131 | semidirect |
| 98. #106 | C2×D131 | semidirect |
| 113. C2×C8 | C4×D131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D1048 | 2 |
| #22553786 | 2 |
| #22553423 | 2 |
| #22553394 | 2 |
| #22553316 | 2 |
| #22553267 | 2 |
| #427×C131 | 2 |
| #2948 | 131 |