Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
492 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 492 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. C22×#14523237 | C2 | semidirect |
| 2. C2×#16861215 | C2 | semidirect |
| 3. #22550452 | C2 | semidirect |
| 5. #22550123 | C2 | semidirect |
| 6. #22550106 | C2 | semidirect |
| 7. #22549884 | C2 | semidirect |
| 8. #22549880 | C2 | semidirect |
| 9. #427×C127 | C2 | semidirect |
| 18. C2×#14523231 | C22 | semidirect |
| 19. C2×C8×D127 | C22 | semidirect |
| 25. #16861189 | C22 | semidirect |
| 28. #16861132 | C22 | semidirect |
| 33. #107×C127 | C22 | semidirect |
| 34. #106×C127 | C22 | semidirect |
| 62. C2×C8×C127 | D4 | semidirect |
| 121. C127 | #3057 | semidirect |
| 128. #427 | D127 | semidirect |
| 152. #107 | C2×D127 | semidirect |
| 153. #106 | C2×D127 | semidirect |
| 180. C2×C8 | D508 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14523237 | 2 |
| C2×#16861215 | 2 |
| #22550452 | 2 |
| #22550445 | 2 |
| #22550123 | 2 |
| #22550106 | 2 |
| #22549884 | 2 |
| #22549880 | 2 |
| #427×C127 | 2 |
| #3057 | 127 |