Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
362 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 115 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. #22550611 | C2 | semidirect |
| 2. #22550587 | C2 | semidirect |
| 3. #22550232 | C2 | semidirect |
| 4. #22550224 | C2 | semidirect |
| 5. #22550179 | C2 | semidirect |
| 6. #22550094 | C2 | semidirect |
| 8. #22550000 | C2 | semidirect |
| 9. C4×#14523235 | C2 | semidirect |
| 10. #22549958 | C2 | semidirect |
| 11. #477×C127 | C2 | semidirect |
| 123. C127 | #3361 | semidirect |
| 129. #477 | D127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22550611 | 2 |
| #22550587 | 2 |
| #22550232 | 2 |
| #22550224 | 2 |
| #22550179 | 2 |
| #22550094 | 2 |
| #22550072 | 2 |
| #22550000 | 2 |
| C4×#14523235 | 2 |
| #22549958 | 2 |
| #477×C127 | 2 |
| #3361 | 127 |