Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
460 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 127 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. C2×Q16×D251 | C2 | semidirect |
| 4. #30631944 | C2 | semidirect |
| 5. #30631943 | C2 | semidirect |
| 6. #30631929 | C2 | semidirect |
| 7. #30631928 | C2 | semidirect |
| 8. #30631925 | C2 | semidirect |
| 9. #30631724 | C2 | semidirect |
| 10. #30631694 | C2 | semidirect |
| 11. #467×C251 | C2 | semidirect |
| 137. C251 | #3059 | semidirect |
| 147. #467 | D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q16×D251 | 2 |
| C2×#22548721 | 2 |
| #30632260 | 2 |
| #30631944 | 2 |
| #30631943 | 2 |
| #30631929 | 2 |
| #30631928 | 2 |
| #30631925 | 2 |
| #30631724 | 2 |
| #30631694 | 2 |
| #467×C251 | 2 |
| #3059 | 251 |