Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
216 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 77 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. #30631736 | C2 | semidirect |
| 4. M16×Dic251 | C2 | semidirect |
| 5. #30631459 | C2 | semidirect |
| 6. #30631448 | C2 | semidirect |
| 21. #101×C251 | C4 | semidirect |
| 22. #100×C251 | C4 | semidirect |
| 95. C251 | #1932 | semidirect |
| 115. #101 | Dic251 | semidirect |
| 116. #100 | Dic251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30631736 | 2 |
| #30631704 | 2 |
| C2×#22548642 | 2 |
| M16×Dic251 | 2 |
| #30631459 | 2 |
| #30631448 | 2 |
| #413×C251 | 2 |
| #1932 | 251 |