Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
178 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 178 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 |
|---|---|---|
| 1. #30632039 | C2 | semidirect |
| 2. #30632037 | C2 | semidirect |
| 6. C8×C251⋊C8 | C2 | semidirect |
| 7. #487×C251 | C2 | semidirect |
| 67. C251 | #1711 | semidirect |
| 71. #487 | D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30632039 | 2 |
| #30632037 | 2 |
| #30632035 | 2 |
| #30632034 | 2 |
| C8×C251⋊C8 | 2 |
| #487×C251 | 2 |
| #1711 | 251 |