Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
816 conjugacy classes of subgroups; only the 269 normal subgroups are shown.
This group has 816 conjugacy classes of subgroups — too many to draw. Only its 269 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×C4⋊Dic251 | C2 | semidirect |
| 3. #30631689 | C2 | direct (N × H) |
| 4. C2×#22548640 | C2 | semidirect |
| 5. C2×#22548637 | C2 | semidirect |
| 6. C22×M16×C251 | C2 | semidirect |
| 9. C2×#16860810 | C4 | semidirect |
| 19. C2×C4⋊Dic251 | C22 | semidirect |
| 20. #22548640 | C22 | semidirect |
| 21. #22548637 | C22 | semidirect |
| 24. C2×M16×C251 | C22 | semidirect |
| 29. #16860810 | C2×C4 | semidirect |
| 32. C2×Dic502 | C2×C4 | semidirect |
| 36. C2×D1004 | C2×C4 | semidirect |
| 65. Dic502 | C22×C4 | semidirect |
| 68. D1004 | C22×C4 | semidirect |
| 110. C2×C251 | #417 | semidirect |
| 115. C251 | C2×#417 | semidirect |
| 118. C22×M16 | D251 | semidirect |
| 134. C2×M16 | C2×D251 | semidirect |
| 227. C2 | #30631689 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#16860810 | 2 |
| C22×C4⋊Dic251 | 2 |
| #30631689 | 2 |
| C2×#22548640 | 2 |
| C2×#22548637 | 2 |
| C22×M16×C251 | 2 |
| C2×#417 | 251 |