Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
348 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 181 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. #30631816 | C2 | semidirect |
| 3. #30631814 | C2 | semidirect |
| 33. C2×C251⋊C8 | Q8 | semidirect |
| 83. C251 | #2961 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30632240 | 2 |
| #30631816 | 2 |
| #30631814 | 2 |
| #30631713 | 2 |
| #30631710 | 2 |
| #30631645 | 2 |
| #30631643 | 2 |
| C2×#22548625 | 2 |
| #424×C251 | 2 |
| #2961 | 251 |