Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
430 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 430 conjugacy classes of subgroups — too many to draw. Only its 125 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. #22550426 | C2 | semidirect |
| 2. #22550166 | C2 | semidirect |
| 3. #22550163 | C2 | semidirect |
| 4. #22550127 | C2 | semidirect |
| 5. #22550071 | C2 | semidirect |
| 6. #22550068 | C2 | semidirect |
| 7. #22549900 | C2 | semidirect |
| 8. #532×C127 | C2 | semidirect |
| 121. C127 | #3253 | semidirect |
| 123. #532 | D127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22550426 | 2 |
| #22550166 | 2 |
| #22550163 | 2 |
| #22550127 | 2 |
| #22550071 | 2 |
| #22550068 | 2 |
| #22549900 | 2 |
| #532×C127 | 2 |
| #3253 | 127 |