Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
386 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 386 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. #30632038 | C2 | semidirect |
| 4. #30632031 | C2 | semidirect |
| 5. #30631967 | C2 | semidirect |
| 6. #30631927 | C2 | semidirect |
| 7. #30631897 | C2 | semidirect |
| 8. #30631846 | C2 | semidirect |
| 9. C8×D1004 | C2 | semidirect |
| 10. #30631680 | C2 | semidirect |
| 11. C4×SD16×C251 | C2 | semidirect |
| 125. C251 | #3302 | semidirect |
| 135. C4×SD16 | D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30632410 | 2 |
| #30632341 | 2 |
| #30632038 | 2 |
| #30632031 | 2 |
| #30631967 | 2 |
| #30631927 | 2 |
| #30631897 | 2 |
| #30631846 | 2 |
| C8×D1004 | 2 |
| #30631680 | 2 |
| C4×SD16×C251 | 2 |
| #3302 | 251 |