Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
456 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 456 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 |
|---|---|---|
| 4. #30631791 | C2 | semidirect |
| 5. #30631779 | C2 | semidirect |
| 11. C2×#16860800 | C4 | semidirect |
| 98. C251 | #2950 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#16860800 | 2 |
| #30632165 | 2 |
| #30632164 | 2 |
| #30631791 | 2 |
| #30631779 | 2 |
| #30631723 | 2 |
| #30631697 | 2 |
| #30631645 | 2 |
| #419×C251 | 2 |
| #2950 | 251 |