Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
252 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 252 conjugacy classes of subgroups — too many to draw. Only its 79 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. #30631735 | C2 | semidirect |
| 5. #30631451 | C2 | semidirect |
| 6. #30631451 | C2 | semidirect |
| 7. #430×C251 | C2 | semidirect |
| 91. C251 | #1858 | semidirect |
| 95. #430 | D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30632453 | 2 |
| #30631735 | 2 |
| #30631669 | 2 |
| #30631655 | 2 |
| #30631451 | 2 |
| #430×C251 | 2 |
| #1858 | 251 |