Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
528 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 528 conjugacy classes of subgroups — too many to draw. Only its 181 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 |
|---|---|---|
| 2. #22550350 | C2 | semidirect |
| 3. #22549987 | C2 | semidirect |
| 4. #22549958 | C2 | semidirect |
| 5. #22549880 | C2 | semidirect |
| 6. #22549831 | C2 | semidirect |
| 7. #427×C127 | C2 | semidirect |
| 9. C2×D1016 | C4 | semidirect |
| 14. #16861171 | C22 | semidirect |
| 17. #16861129 | C22 | semidirect |
| 18. #16861119 | C22 | semidirect |
| 19. C8×Dic127 | C22 | semidirect |
| 22. #107×C127 | C22 | semidirect |
| 23. #106×C127 | C22 | semidirect |
| 27. C2×D508 | C2×C4 | semidirect |
| 30. D1016 | C2×C4 | semidirect |
| 31. D1016 | C2×C4 | semidirect |
| 39. C2×C8×C127 | C2×C4 | semidirect |
| 78. C127 | #2948 | semidirect |
| 83. #427 | D127 | semidirect |
| 97. #107 | C2×D127 | semidirect |
| 98. #106 | C2×D127 | semidirect |
| 113. C2×C8 | C4×D127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D1016 | 2 |
| #22550350 | 2 |
| #22549987 | 2 |
| #22549958 | 2 |
| #22549880 | 2 |
| #22549831 | 2 |
| #427×C127 | 2 |
| #2948 | 127 |