Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
454 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 454 conjugacy classes of subgroups — too many to draw. Only its 125 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. #22550690 | C2 | semidirect |
| 2. #22550688 | C2 | semidirect |
| 3. #22550678 | C2 | semidirect |
| 4. #22550260 | C2 | semidirect |
| 5. #22550152 | C2 | semidirect |
| 6. #22550147 | C2 | semidirect |
| 7. #22550139 | C2 | semidirect |
| 8. #22550055 | C2 | semidirect |
| 9. #22550050 | C2 | semidirect |
| 10. #22549994 | C2 | semidirect |
| 11. #443×C127 | C2 | semidirect |
| 12. #16861256 | C22 | semidirect |
| 16. #16861239 | C22 | semidirect |
| 19. #16861237 | C22 | semidirect |
| 26. C2×Dic508 | C22 | semidirect |
| 29. C2×#14523237 | C22 | semidirect |
| 33. #16861215 | C22 | semidirect |
| 34. #16861197 | C22 | semidirect |
| 35. #16861145 | C22 | semidirect |
| 37. #16861137 | C22 | semidirect |
| 38. #16861127 | C22 | semidirect |
| 39. #16861125 | C22 | semidirect |
| 41. #131×C127 | C22 | semidirect |
| 42. #108×C127 | C22 | semidirect |
| 43. #104×C127 | C22 | semidirect |
| 44. C4×C8×C127 | C22 | semidirect |
| 150. C127 | #3290 | semidirect |
| 161. #443 | D127 | semidirect |
| 185. #131 | C2×D127 | semidirect |
| 188. #108 | C2×D127 | semidirect |
| 191. #104 | C2×D127 | semidirect |
| 194. C4×C8 | C2×D127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22550690 | 2 |
| #22550688 | 2 |
| #22550678 | 2 |
| #22550260 | 2 |
| #22550152 | 2 |
| #22550147 | 2 |
| #22550139 | 2 |
| #22550055 | 2 |
| #22550050 | 2 |
| #22549994 | 2 |
| #443×C127 | 2 |
| #3290 | 127 |