Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
812 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 812 conjugacy classes of subgroups — too many to draw. Only its 165 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. C22×#16860809 | C2 | semidirect |
| 2. C22×#16860798 | C2 | semidirect |
| 3. C2×#22548686 | C2 | semidirect |
| 4. #30631829 | C2 | direct (N × H) |
| 5. C2×#22548640 | C2 | semidirect |
| 6. C2×#22548636 | C2 | semidirect |
| 7. C2×(C2×D251)⋊C8 | C2 | semidirect |
| 8. C22×D8×C251 | C2 | semidirect |
| 12. C2×#16860809 | C22 | semidirect |
| 19. C2×#16860798 | C22 | semidirect |
| 22. #22548686 | C22 | semidirect |
| 25. #22548640 | C22 | semidirect |
| 26. #22548636 | C22 | semidirect |
| 27. (C2×D251)⋊C8 | C22 | semidirect |
| 31. C2×D8×C251 | C22 | semidirect |
| 39. C2×Dic502 | D4 | semidirect |
| 67. C2×D4×C251 | D4 | semidirect |
| 80. Dic502 | C2×D4 | semidirect |
| 108. D4×C251 | C2×D4 | semidirect |
| 138. C2×C251 | #449 | semidirect |
| 143. C251 | C2×#449 | semidirect |
| 147. C22×D8 | D251 | semidirect |
| 167. C2×D8 | C2×D251 | semidirect |
| 196. C2×D4 | C22⋊D251 | semidirect |
| 241. D4 | C2×C22⋊D251 | semidirect |
| 283. C2 | #30631829 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#16860809 | 2 |
| C22×#16860798 | 2 |
| C2×#22548686 | 2 |
| #30631829 | 2 |
| C2×#22548640 | 2 |
| C2×#22548636 | 2 |
| C2×(C2×D251)⋊C8 | 2 |
| C22×D8×C251 | 2 |
| C2×#449 | 251 |