Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
188 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 188 conjugacy classes of subgroups — too many to draw. Only its 57 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. #30632059 | C2 | semidirect |
| 2. #30631967 | C2 | semidirect |
| 3. D4×C251⋊C8 | C2 | semidirect |
| 4. #30631437 | C2 | semidirect |
| 5. #30631432 | C2 | semidirect |
| 6. #30631431 | C2 | semidirect |
| 49. C251⋊C8 | D8 | semidirect |
| 58. D4×C251 | SD16 | semidirect |
| 85. C251 | #1665 | semidirect |
| 139. D4 | #16860798 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30632059 | 2 |
| #30631967 | 2 |
| D4×C251⋊C8 | 2 |
| #30631437 | 2 |
| #30631432 | 2 |
| #30631431 | 2 |
| #459×C251 | 2 |
| #1665 | 251 |