Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
374 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 374 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 |
|---|---|---|
| 1. #30632410 | C2 | semidirect |
| 3. #30632092 | C2 | semidirect |
| 4. #30632021 | C2 | semidirect |
| 5. #30632009 | C2 | semidirect |
| 6. #30631972 | C2 | semidirect |
| 7. #30631967 | C2 | semidirect |
| 8. #30631930 | C2 | semidirect |
| 9. #30631766 | C2 | semidirect |
| 10. #30631726 | C2 | semidirect |
| 11. C4×SD16×C251 | C2 | semidirect |
| 99. C8×C251 | #41 | semidirect |
| 122. C251 | #3353 | semidirect |
| 132. C4×SD16 | D251 | semidirect |
| 222. C8 | #16860810 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30632410 | 2 |
| #30632342 | 2 |
| #30632092 | 2 |
| #30632021 | 2 |
| #30632009 | 2 |
| #30631972 | 2 |
| #30631967 | 2 |
| #30631930 | 2 |
| #30631766 | 2 |
| #30631726 | 2 |
| C4×SD16×C251 | 2 |
| #3353 | 251 |