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. #22550591 | C2 | semidirect |
| 2. #22550548 | C2 | semidirect |
| 3. #22550223 | C2 | semidirect |
| 4. #22550202 | C2 | semidirect |
| 5. #22550171 | C2 | semidirect |
| 6. #22550111 | C2 | semidirect |
| 7. #22550071 | C2 | semidirect |
| 8. #22550020 | C2 | semidirect |
| 9. C8×D508 | C2 | semidirect |
| 10. #22549871 | C2 | semidirect |
| 11. C4×SD16×C127 | C2 | semidirect |
| 133. C127 | #3305 | semidirect |
| 142. C4×SD16 | D127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22550591 | 2 |
| #22550548 | 2 |
| #22550223 | 2 |
| #22550202 | 2 |
| #22550171 | 2 |
| #22550111 | 2 |
| #22550071 | 2 |
| #22550020 | 2 |
| C8×D508 | 2 |
| #22549871 | 2 |
| C4×SD16×C127 | 2 |
| #3305 | 127 |