Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
446 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 446 conjugacy classes of subgroups — too many to draw. Only its 129 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. C2×#22548746 | C2 | semidirect |
| 3. C2×#22548746 | C2 | semidirect |
| 4. #30632453 | C2 | semidirect |
| 5. #30631961 | C2 | semidirect |
| 6. #30631953 | C2 | semidirect |
| 7. #30631735 | C2 | semidirect |
| 8. #30631669 | C2 | semidirect |
| 9. C2×#101×C251 | C2 | semidirect |
| 22. C2×#16860800 | C22 | semidirect |
| 24. C2×#16860797 | C22 | semidirect |
| 30. #22548650 | C22 | semidirect |
| 31. #22548633 | C22 | semidirect |
| 32. #22548631 | C22 | semidirect |
| 36. #101×C251 | C22 | semidirect |
| 142. C251 | #3069 | semidirect |
| 152. C2×#101 | D251 | semidirect |
| 178. #101 | C2×D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30632487 | 2 |
| C2×#22548746 | 2 |
| #30632453 | 2 |
| #30631961 | 2 |
| #30631953 | 2 |
| #30631735 | 2 |
| #30631669 | 2 |
| C2×#101×C251 | 2 |
| #3069 | 251 |