Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
362 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 141 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. #30631991 | C2 | semidirect |
| 3. #30631991 | C2 | semidirect |
| 4. #30631979 | C2 | semidirect |
| 5. #30631969 | C2 | semidirect |
| 43. C2×Dic502 | Q8 | semidirect |
| 116. C251 | #3082 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30632164 | 2 |
| #30631991 | 2 |
| #30631979 | 2 |
| #30631969 | 2 |
| #30631727 | 2 |
| #30631723 | 2 |
| #30631714 | 2 |
| #30631695 | 2 |
| C2×#22548638 | 2 |
| #544×C251 | 2 |
| #3082 | 251 |