Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
180 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 73 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. #30631811 | C2 | semidirect |
| 4. #30631417 | C2 | semidirect |
| 6. C8×C251⋊C8 | C2 | semidirect |
| 7. #334×C251 | C2 | semidirect |
| 26. #16860799 | C8 | semidirect |
| 43. Dic502 | C2×C8 | semidirect |
| 53. C251⋊C8 | SD16 | semidirect |
| 60. C8×C251 | C2×C8 | semidirect |
| 77. C251 | C8×SD16 | semidirect |
| 82. #334 | D251 | semidirect |
| 138. C8 | C8×D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30631811 | 2 |
| C4×#16860799 | 2 |
| #30631752 | 2 |
| #30631417 | 2 |
| #30631414 | 2 |
| C8×C251⋊C8 | 2 |
| #334×C251 | 2 |
| C8×SD16 | 251 |