Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
492 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 189 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. #30632164 | C2 | semidirect |
| 4. #30631789 | C2 | semidirect |
| 5. C4×#16860799 | C2 | semidirect |
| 6. #30631725 | C2 | semidirect |
| 7. #30631697 | C2 | semidirect |
| 9. #405×C251 | C2 | semidirect |
| 12. C2×#16860799 | C4 | semidirect |
| 15. C4×Dic502 | C22 | semidirect |
| 23. #22548649 | C22 | semidirect |
| 24. #22548647 | C22 | semidirect |
| 25. #22548640 | C22 | semidirect |
| 30. #97×C251 | C22 | semidirect |
| 31. C4×C8×C251 | C22 | semidirect |
| 35. C2×Dic502 | C2×C4 | semidirect |
| 43. #16860799 | C2×C4 | semidirect |
| 44. #16860799 | C2×C4 | semidirect |
| 56. C2×C8×C251 | C2×C4 | semidirect |
| 103. C251 | #2949 | semidirect |
| 113. #405 | D251 | semidirect |
| 134. #97 | C2×D251 | semidirect |
| 135. C4×C8 | C2×D251 | semidirect |
| 151. C2×C8 | C4×D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#16860799 | 2 |
| #30632164 | 2 |
| #30632161 | 2 |
| #30631789 | 2 |
| C4×#16860799 | 2 |
| #30631725 | 2 |
| #30631697 | 2 |
| #30631693 | 2 |
| #405×C251 | 2 |
| #2949 | 251 |