Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
292 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 89 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. C2×#22548650 | C2 | semidirect |
| 4. #30631452 | C2 | semidirect |
| 5. #341×C251 | C2 | semidirect |
| 56. C2×D251 | #108 | semidirect |
| 65. C251 | #1810 | semidirect |
| 71. #341 | D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C8×D251 | 2 |
| C2×#22548650 | 2 |
| #30631650 | 2 |
| #30631452 | 2 |
| #341×C251 | 2 |
| #1810 | 251 |