Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
348 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 348 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 |
|---|---|---|
| 2. #30632416 | C2 | semidirect |
| 3. #30632043 | C2 | semidirect |
| 5. #30631990 | C2 | semidirect |
| 6. #30631972 | C2 | semidirect |
| 7. #30631911 | C2 | semidirect |
| 9. C8×Dic502 | C2 | semidirect |
| 10. #30631772 | C2 | semidirect |
| 11. C4×Q16×C251 | C2 | semidirect |
| 117. C251 | #3365 | semidirect |
| 128. C4×Q16 | D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30632422 | 2 |
| #30632416 | 2 |
| #30632043 | 2 |
| #30632034 | 2 |
| #30631990 | 2 |
| #30631972 | 2 |
| #30631911 | 2 |
| #30631887 | 2 |
| C8×Dic502 | 2 |
| #30631772 | 2 |
| C4×Q16×C251 | 2 |
| #3365 | 251 |