Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
216 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 69 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. C4×#16860794 | C2 | semidirect |
| 3. #30631428 | C2 | semidirect |
| 4. #30631426 | C2 | semidirect |
| 5. #432×C251 | C2 | semidirect |
| 90. C251 | #1529 | semidirect |
| 93. #432 | D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30632221 | 2 |
| C4×#16860794 | 2 |
| #30631428 | 2 |
| #30631426 | 2 |
| #432×C251 | 2 |
| #1529 | 251 |