Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
392 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 117 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. #125×D251 | C2 | semidirect |
| 3. #30632055 | C2 | semidirect |
| 4. #30632053 | C2 | semidirect |
| 5. #30632052 | C2 | semidirect |
| 6. #30632043 | C2 | semidirect |
| 7. #30631687 | C2 | semidirect |
| 8. #30631639 | C2 | semidirect |
| 9. #491×C251 | C2 | semidirect |
| 90. C251 | #3142 | semidirect |
| 95. #491 | D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30632238 | 2 |
| #125×D251 | 2 |
| #30632055 | 2 |
| #30632053 | 2 |
| #30632052 | 2 |
| #30632043 | 2 |
| #30631687 | 2 |
| #30631639 | 2 |
| #491×C251 | 2 |
| #3142 | 251 |