Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
142 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 142 conjugacy classes of subgroups — too many to draw. Only its 51 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. #30632091 | C2 | semidirect |
| 3. #30631515 | C2 | semidirect |
| 4. #30631514 | C2 | semidirect |
| 5. Dic251⋊C16 | C2 | semidirect |
| 30. D8×C251 | Q8 | semidirect |
| 63. C251 | #2226 | semidirect |
| 87. D8 | Dic502 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30632091 | 2 |
| D8×Dic251 | 2 |
| #30631515 | 2 |
| #30631514 | 2 |
| Dic251⋊C16 | 2 |
| #30631488 | 2 |
| #357×C251 | 2 |
| #2226 | 251 |