Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
372 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 133 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. #22550504 | C2 | semidirect |
| 3. #22550245 | C2 | semidirect |
| 4. #22550236 | C2 | semidirect |
| 5. #22550231 | C2 | semidirect |
| 6. #22550227 | C2 | semidirect |
| 7. #22549886 | C2 | semidirect |
| 10. C2×#16861134 | C2 | semidirect |
| 11. #405×C127 | C2 | semidirect |
| 128. C127 | #3137 | semidirect |
| 139. #405 | D127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22550504 | 2 |
| #22550452 | 2 |
| #22550245 | 2 |
| #22550236 | 2 |
| #22550231 | 2 |
| #22550227 | 2 |
| #22549886 | 2 |
| #22549878 | 2 |
| #22549873 | 2 |
| C2×#16861134 | 2 |
| #405×C127 | 2 |
| #3137 | 127 |