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×#16861217 | C2 | semidirect |
| 3. #22550457 | C2 | semidirect |
| 4. #22550445 | C2 | semidirect |
| 5. #22550130 | C2 | semidirect |
| 6. #22550123 | C2 | semidirect |
| 7. #22550113 | C2 | semidirect |
| 8. #22550106 | C2 | semidirect |
| 9. #22549870 | C2 | semidirect |
| 10. C2×#16861129 | C2 | semidirect |
| 11. #428×C127 | C2 | semidirect |
| 19. C2×#14523231 | C22 | semidirect |
| 21. C2×C8×D127 | C22 | semidirect |
| 25. #16861189 | C22 | semidirect |
| 29. #16861184 | C22 | semidirect |
| 32. #16861132 | C22 | semidirect |
| 33. #16861132 | C22 | semidirect |
| 36. #16861129 | C22 | semidirect |
| 37. #16861129 | C22 | semidirect |
| 41. #107×C127 | C22 | semidirect |
| 42. #106×C127 | C22 | semidirect |
| 77. M16×C127 | D4 | semidirect |
| 152. C127 | #3062 | semidirect |
| 161. #428 | D127 | semidirect |
| 187. #107 | C2×D127 | semidirect |
| 188. #106 | C2×D127 | semidirect |
| 220. M16 | D508 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16861237 | 2 |
| C2×#16861217 | 2 |
| #22550457 | 2 |
| #22550445 | 2 |
| #22550130 | 2 |
| #22550123 | 2 |
| #22550113 | 2 |
| #22550106 | 2 |
| #22549870 | 2 |
| C2×#16861129 | 2 |
| #428×C127 | 2 |
| #3062 | 127 |