Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
184 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 184 conjugacy classes of subgroups — too many to draw. Only its 53 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. #30631887 | C2 | semidirect |
| 3. #30631818 | C2 | semidirect |
| 4. #30631437 | C2 | semidirect |
| 5. #30631431 | C2 | semidirect |
| 6. #30631430 | C2 | semidirect |
| 7. #460×C251 | C2 | semidirect |
| 52. C251⋊C8 | SD16 | semidirect |
| 86. C251 | #1688 | semidirect |
| 90. #460 | D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30632063 | 2 |
| #30631887 | 2 |
| #30631818 | 2 |
| #30631437 | 2 |
| #30631431 | 2 |
| #30631430 | 2 |
| #460×C251 | 2 |
| #1688 | 251 |