Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
504 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 504 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. C2×#16861231 | C2 | semidirect |
| 3. #22550445 | C2 | semidirect |
| 4. #22550356 | C2 | semidirect |
| 5. #22550099 | C2 | semidirect |
| 6. #22550092 | C2 | semidirect |
| 7. #22550077 | C2 | semidirect |
| 8. #22550072 | C2 | semidirect |
| 9. #22549878 | C2 | semidirect |
| 10. C2×#16861131 | C2 | semidirect |
| 11. #424×C127 | C2 | semidirect |
| 17. C2×Dic508 | C22 | semidirect |
| 19. C2×#14523237 | C22 | semidirect |
| 20. C2×#14523237 | C22 | semidirect |
| 22. C2×D1016 | C22 | semidirect |
| 28. C4×Dic254 | C22 | semidirect |
| 29. C4×D508 | C22 | semidirect |
| 34. #16861134 | C22 | semidirect |
| 37. #16861131 | C22 | semidirect |
| 41. C4⋊C8×C127 | C22 | semidirect |
| 42. C4⋊C8×C127 | C22 | semidirect |
| 47. #14523248 | D4 | semidirect |
| 155. C127 | #3045 | semidirect |
| 164. #424 | D127 | semidirect |
| 192. C4⋊C8 | C2×D127 | semidirect |
| 193. 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 |
| C2×#16861231 | 2 |
| #22550445 | 2 |
| #22550356 | 2 |
| #22550099 | 2 |
| #22550092 | 2 |
| #22550077 | 2 |
| #22550072 | 2 |
| #22549878 | 2 |
| C2×#16861131 | 2 |
| #424×C127 | 2 |
| #3045 | 127 |