Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
444 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 444 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. #30632504 | C2 | semidirect |
| 2. #30632503 | C2 | semidirect |
| 3. #30632500 | C2 | semidirect |
| 4. #30632065 | C2 | semidirect |
| 5. #30631963 | C2 | semidirect |
| 6. #30631961 | C2 | semidirect |
| 7. #30631872 | C2 | semidirect |
| 8. #30631868 | C2 | semidirect |
| 9. #30631803 | C2 | semidirect |
| 10. #30631802 | C2 | semidirect |
| 11. #473×C251 | C2 | semidirect |
| 146. C251 | #3293 | semidirect |
| 154. #473 | D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30632504 | 2 |
| #30632503 | 2 |
| #30632500 | 2 |
| #30632065 | 2 |
| #30631963 | 2 |
| #30631961 | 2 |
| #30631872 | 2 |
| #30631868 | 2 |
| #30631803 | 2 |
| #30631802 | 2 |
| #473×C251 | 2 |
| #3293 | 251 |