Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
172 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 172 conjugacy classes of subgroups — too many to draw. Only its 57 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 |
|---|---|---|
| 3. #30631440 | C2 | semidirect |
| 4. #30631433 | C2 | semidirect |
| 5. #500×C251 | C2 | semidirect |
| 46. C8×C251 | SD16 | semidirect |
| 62. C251 | #1673 | semidirect |
| 64. #500 | D251 | semidirect |
| 109. C8 | #16860797 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30631889 | 2 |
| C8×D1004 | 2 |
| #30631440 | 2 |
| #30631433 | 2 |
| #500×C251 | 2 |
| #1673 | 251 |