Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
996 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 996 conjugacy classes of subgroups — too many to draw. Only its 173 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. C22×#16860799 | C2 | semidirect |
| 3. C22×#16860798 | C2 | semidirect |
| 4. C2×#22548695 | C2 | semidirect |
| 5. #30631839 | C2 | direct (N × H) |
| 6. C2×#22548635 | C2 | semidirect |
| 7. C2×(C2×D251)⋊C8 | C2 | semidirect |
| 8. C2×#102×C251 | C2 | semidirect |
| 10. C22×Dic502 | C22 | semidirect |
| 19. C2×#16860799 | C22 | semidirect |
| 21. C2×#16860798 | C22 | semidirect |
| 22. C22×C251⋊C8 | C22 | semidirect |
| 24. #22548695 | C22 | semidirect |
| 27. #22548635 | C22 | semidirect |
| 28. (C2×D251)⋊C8 | C22 | semidirect |
| 30. C22×C8×C251 | C22 | semidirect |
| 31. C2×C4⋊C4×C251 | C22 | semidirect |
| 32. #102×C251 | C22 | semidirect |
| 42. C2×Dic502 | C23 | semidirect |
| 61. C2×C251⋊C8 | C23 | semidirect |
| 72. C2×C8×C251 | C23 | semidirect |
| 74. C4⋊C4×C251 | C23 | semidirect |
| 85. C22×D251 | SD16 | semidirect |
| 133. C2×D251 | C2×SD16 | semidirect |
| 141. C2×C251 | #450 | semidirect |
| 147. C251 | C2×#450 | semidirect |
| 155. C2×#102 | D251 | semidirect |
| 172. C22×C8 | C2×D251 | semidirect |
| 176. C2×C4⋊C4 | C2×D251 | semidirect |
| 179. #102 | C2×D251 | semidirect |
| 218. C2×C8 | C22×D251 | semidirect |
| 221. C4⋊C4 | C22×D251 | semidirect |
| 291. C2 | #30631839 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D4×D251 | 2 |
| C22×#16860799 | 2 |
| C22×#16860798 | 2 |
| C2×#22548695 | 2 |
| #30631839 | 2 |
| C2×#22548635 | 2 |
| C2×(C2×D251)⋊C8 | 2 |
| C2×#102×C251 | 2 |
| C2×#450 | 251 |