Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
526 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 526 conjugacy classes of subgroups — too many to draw. Only its 141 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×#16861237 | C2 | semidirect |
| 2. C22×D1016 | C2 | semidirect |
| 3. #22550445 | C2 | semidirect |
| 4. #22550350 | C2 | semidirect |
| 5. #22550092 | C2 | semidirect |
| 6. #22550072 | C2 | semidirect |
| 7. #22549882 | C2 | semidirect |
| 8. #22549873 | C2 | semidirect |
| 9. #424×C127 | C2 | semidirect |
| 14. C2×#14523237 | C22 | semidirect |
| 17. C2×D1016 | C22 | semidirect |
| 18. #16861206 | C22 | semidirect |
| 19. #16861197 | C22 | semidirect |
| 22. C4×D508 | C22 | semidirect |
| 26. #16861134 | C22 | semidirect |
| 27. #16861131 | C22 | semidirect |
| 28. #16861131 | C22 | semidirect |
| 32. C4⋊C8×C127 | C22 | semidirect |
| 44. C2×D508 | D4 | semidirect |
| 122. C127 | #3041 | semidirect |
| 129. #424 | D127 | semidirect |
| 151. C4⋊C8 | C2×D127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16861237 | 2 |
| C22×D1016 | 2 |
| #22550445 | 2 |
| #22550350 | 2 |
| #22550092 | 2 |
| #22550072 | 2 |
| #22549882 | 2 |
| #22549873 | 2 |
| #424×C127 | 2 |
| #3041 | 127 |