Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
524 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 524 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×D1016 | C2 | semidirect |
| 2. C2×#16861215 | C2 | semidirect |
| 3. #22550445 | C2 | semidirect |
| 4. #22550130 | C2 | semidirect |
| 5. #22550113 | C2 | semidirect |
| 6. #22549880 | C2 | semidirect |
| 7. #427×C127 | C2 | semidirect |
| 15. C2×#14523231 | C22 | semidirect |
| 16. C2×C8×D127 | C22 | semidirect |
| 19. #16861184 | C22 | semidirect |
| 21. #16861129 | C22 | semidirect |
| 24. #107×C127 | C22 | semidirect |
| 25. #106×C127 | C22 | semidirect |
| 46. C2×C8×C127 | D4 | semidirect |
| 94. C127 | #3058 | semidirect |
| 100. #427 | D127 | semidirect |
| 117. #107 | C2×D127 | semidirect |
| 118. #106 | C2×D127 | semidirect |
| 139. C2×C8 | D508 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D1016 | 2 |
| C2×#16861215 | 2 |
| #22550445 | 2 |
| #22550130 | 2 |
| #22550113 | 2 |
| #22549880 | 2 |
| #427×C127 | 2 |
| #3058 | 127 |