Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
360 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 113 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. #22550579 | C2 | semidirect |
| 2. #22550203 | C2 | semidirect |
| 3. #22550191 | C2 | semidirect |
| 4. #22550173 | C2 | semidirect |
| 5. #22550130 | C2 | semidirect |
| 6. C4×D1016 | C2 | semidirect |
| 7. #22549955 | C2 | semidirect |
| 8. #22549915 | C2 | semidirect |
| 9. #499×C127 | C2 | semidirect |
| 103. C127 | #3355 | semidirect |
| 105. #499 | D127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22550579 | 2 |
| #22550203 | 2 |
| #22550191 | 2 |
| #22550173 | 2 |
| #22550130 | 2 |
| C4×D1016 | 2 |
| #22549955 | 2 |
| #22549915 | 2 |
| #499×C127 | 2 |
| #3355 | 127 |