Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
452 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 452 conjugacy classes of subgroups — too many to draw. Only its 123 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. #30632486 | C2 | semidirect |
| 2. C2×#22548738 | C2 | semidirect |
| 3. #131×D251 | C2 | semidirect |
| 4. #30631959 | C2 | semidirect |
| 5. #30631958 | C2 | semidirect |
| 6. #30631957 | C2 | semidirect |
| 7. #30631953 | C2 | semidirect |
| 8. #30631952 | C2 | semidirect |
| 9. #108×D251 | C2 | semidirect |
| 10. #30631670 | C2 | semidirect |
| 11. #473×C251 | C2 | semidirect |
| 25. C2×#16860797 | C22 | semidirect |
| 26. C2×D2008 | C22 | semidirect |
| 37. #22548651 | C22 | semidirect |
| 38. #22548650 | C22 | semidirect |
| 39. #22548634 | C22 | semidirect |
| 40. #22548631 | C22 | semidirect |
| 41. #22548631 | C22 | semidirect |
| 43. C2×Q16×C251 | C22 | semidirect |
| 45. #108×C251 | C22 | semidirect |
| 46. #101×C251 | C22 | semidirect |
| 166. C251 | #3067 | semidirect |
| 172. #473 | D251 | semidirect |
| 193. C2×Q16 | C2×D251 | semidirect |
| 209. #108 | C2×D251 | semidirect |
| 211. #101 | C2×D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30632486 | 2 |
| C2×#22548738 | 2 |
| #131×D251 | 2 |
| #30631959 | 2 |
| #30631958 | 2 |
| #30631957 | 2 |
| #30631953 | 2 |
| #30631952 | 2 |
| #108×D251 | 2 |
| #30631670 | 2 |
| #473×C251 | 2 |
| #3067 | 251 |