Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
144 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 144 conjugacy classes of subgroups — too many to draw. Only its 65 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 |
|---|---|---|
| 1. #30632103 | C2 | semidirect |
| 3. #30631508 | C2 | semidirect |
| 4. #30631470 | C2 | semidirect |
| 5. #346×C251 | C2 | semidirect |
| 49. C251 | #2171 | semidirect |
| 55. #346 | D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30632103 | 2 |
| #30631805 | 2 |
| #30631508 | 2 |
| #30631470 | 2 |
| #346×C251 | 2 |
| #2171 | 251 |