Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
444 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 125 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. #30632502 | C2 | semidirect |
| 2. #30632501 | C2 | semidirect |
| 3. #30632065 | C2 | semidirect |
| 4. #30631962 | C2 | semidirect |
| 5. #30631960 | C2 | semidirect |
| 6. #30631959 | C2 | semidirect |
| 7. #30631870 | C2 | semidirect |
| 8. #30631868 | C2 | semidirect |
| 9. #30631804 | C2 | semidirect |
| 10. #30631802 | C2 | semidirect |
| 11. #578×C251 | C2 | semidirect |
| 146. C251 | #3293 | semidirect |
| 150. #578 | D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30632502 | 2 |
| #30632501 | 2 |
| #30632065 | 2 |
| #30631962 | 2 |
| #30631960 | 2 |
| #30631959 | 2 |
| #30631870 | 2 |
| #30631868 | 2 |
| #30631804 | 2 |
| #30631802 | 2 |
| #578×C251 | 2 |
| #3293 | 251 |