Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
172 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 172 conjugacy classes of subgroups — too many to draw. Only its 73 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 |
|---|---|---|
| 16. #22548625 | C4 | semidirect |
| 17. C8×Dic251 | C4 | semidirect |
| 78. C251 | #1833 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22548650 | 2 |
| #30631723 | 2 |
| #30631645 | 2 |
| #30631458 | 2 |
| #30631444 | 2 |
| #30631443 | 2 |
| #344×C251 | 2 |
| #1833 | 251 |