Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
408 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 408 conjugacy classes of subgroups — too many to draw. Only its 123 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. #22550547 | C2 | semidirect |
| 3. #22550223 | C2 | semidirect |
| 4. #22550201 | C2 | semidirect |
| 5. #22550172 | C2 | semidirect |
| 6. #22550112 | C2 | semidirect |
| 7. #22550072 | C2 | semidirect |
| 8. #22550023 | C2 | semidirect |
| 9. C4×#14523237 | C2 | semidirect |
| 10. #22549873 | C2 | semidirect |
| 11. C8×D4×C127 | C2 | semidirect |
| 133. C127 | #3305 | semidirect |
| 143. C8×D4 | D127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22550591 | 2 |
| #22550547 | 2 |
| #22550223 | 2 |
| #22550201 | 2 |
| #22550172 | 2 |
| #22550112 | 2 |
| #22550072 | 2 |
| #22550023 | 2 |
| C4×#14523237 | 2 |
| #22549873 | 2 |
| C8×D4×C127 | 2 |
| #3305 | 127 |