Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
170 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 170 conjugacy classes of subgroups — too many to draw. Only its 49 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. #30632033 | C2 | semidirect |
| 2. #30631978 | C2 | semidirect |
| 4. #30631764 | C2 | semidirect |
| 5. #30631439 | C2 | semidirect |
| 6. #30631435 | C2 | semidirect |
| 7. #331×C251 | C2 | semidirect |
| 82. C251 | #1697 | semidirect |
| 90. #331 | D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30632033 | 2 |
| #30631978 | 2 |
| #30631879 | 2 |
| #30631764 | 2 |
| #30631439 | 2 |
| #30631435 | 2 |
| #331×C251 | 2 |
| #1697 | 251 |