Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
322 conjugacy classes of subgroups; only the 161 normal subgroups are shown.
This group has 322 conjugacy classes of subgroups — too many to draw. Only its 161 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 |
|---|---|---|
| 2. #30631817 | C2 | semidirect |
| 3. #30631816 | C2 | semidirect |
| 4. C8×Dic502 | C2 | semidirect |
| 81. C251 | #2985 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30632244 | 2 |
| #30631817 | 2 |
| #30631816 | 2 |
| C8×Dic502 | 2 |
| #30631745 | 2 |
| #30631744 | 2 |
| #431×C251 | 2 |
| #2985 | 251 |