Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
360 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 121 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. #30632383 | C2 | semidirect |
| 2. #30632089 | C2 | semidirect |
| 3. #30632012 | C2 | semidirect |
| 4. #30632001 | C2 | semidirect |
| 5. #30631988 | C2 | semidirect |
| 6. #30631940 | C2 | semidirect |
| 7. C4×D2008 | C2 | semidirect |
| 8. #30631729 | C2 | semidirect |
| 9. #436×C251 | C2 | semidirect |
| 102. C251 | #3355 | semidirect |
| 111. #436 | D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30632383 | 2 |
| #30632089 | 2 |
| #30632012 | 2 |
| #30632001 | 2 |
| #30631988 | 2 |
| #30631940 | 2 |
| C4×D2008 | 2 |
| #30631729 | 2 |
| #436×C251 | 2 |
| #3355 | 251 |