Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
176 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 176 conjugacy classes of subgroups — too many to draw. Only its 71 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. #30631408 | C2 | semidirect |
| 7. #335×C251 | C2 | semidirect |
| 26. #16860799 | C8 | semidirect |
| 43. Dic502 | C2×C8 | semidirect |
| 60. C8×C251 | C2×C8 | semidirect |
| 77. C251 | SD16⋊C8 | semidirect |
| 82. #335 | 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 |
| #30631408 | 2 |
| #335×C251 | 2 |
| SD16⋊C8 | 251 |