Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
242 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 242 conjugacy classes of subgroups — too many to draw. Only its 61 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. #30632064 | C2 | semidirect |
| 2. #30632063 | C2 | semidirect |
| 3. #30632063 | C2 | semidirect |
| 4. #30632061 | C2 | semidirect |
| 5. #30632035 | C2 | semidirect |
| 6. #30631409 | C2 | semidirect |
| 7. #486×C251 | C2 | semidirect |
| 50. C251⋊C8 | D8 | semidirect |
| 81. C251 | #1721 | semidirect |
| 88. #486 | D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30632064 | 2 |
| #30632063 | 2 |
| #30632061 | 2 |
| #30632035 | 2 |
| #30631409 | 2 |
| #486×C251 | 2 |
| #1721 | 251 |