Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
396 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 396 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. #22550599 | C2 | semidirect |
| 3. #22550223 | C2 | semidirect |
| 4. #22550203 | C2 | semidirect |
| 5. #22550161 | C2 | semidirect |
| 6. #22550108 | C2 | semidirect |
| 7. #22550076 | C2 | semidirect |
| 8. #22550037 | C2 | semidirect |
| 9. C8×D508 | C2 | semidirect |
| 10. #22549871 | C2 | semidirect |
| 11. C4×Q16×C127 | C2 | semidirect |
| 128. C127 | #3304 | semidirect |
| 137. C4×Q16 | D127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22550599 | 2 |
| #22550548 | 2 |
| #22550223 | 2 |
| #22550203 | 2 |
| #22550161 | 2 |
| #22550108 | 2 |
| #22550076 | 2 |
| #22550037 | 2 |
| C8×D508 | 2 |
| #22549871 | 2 |
| C4×Q16×C127 | 2 |
| #3304 | 127 |