Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
408 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 408 conjugacy classes of subgroups — too many to draw. Only its 117 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. #22550592 | C2 | semidirect |
| 2. #22550548 | C2 | semidirect |
| 3. #22550224 | C2 | semidirect |
| 4. #22550203 | C2 | semidirect |
| 5. #22550113 | C2 | semidirect |
| 6. #22550072 | C2 | semidirect |
| 7. #22550024 | C2 | semidirect |
| 8. C4×#14523235 | C2 | semidirect |
| 9. #22549941 | C2 | semidirect |
| 10. #22549871 | C2 | semidirect |
| 11. #477×C127 | C2 | semidirect |
| 133. C127 | #3305 | semidirect |
| 138. #477 | D127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22550592 | 2 |
| #22550548 | 2 |
| #22550224 | 2 |
| #22550203 | 2 |
| #22550113 | 2 |
| #22550072 | 2 |
| #22550024 | 2 |
| C4×#14523235 | 2 |
| #22549941 | 2 |
| #22549871 | 2 |
| #477×C127 | 2 |
| #3305 | 127 |