Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
180 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 77 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. C8×Dic502 | C2 | semidirect |
| 3. #30631437 | C2 | semidirect |
| 4. #30631417 | C2 | semidirect |
| 6. C8×C251⋊C8 | C2 | semidirect |
| 24. #16860798 | C8 | direct (N × H) |
| 42. Dic502 | C2×C8 | semidirect |
| 48. C251⋊C8 | C2×C8 | semidirect |
| 60. C8×C251 | SD16 | semidirect |
| 77. C251 | C8×SD16 | semidirect |
| 138. C8 | #16860798 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C8×Dic502 | 2 |
| C4×#16860798 | 2 |
| #30631437 | 2 |
| #30631417 | 2 |
| D4⋊(C251⋊C8) | 2 |
| C8×C251⋊C8 | 2 |
| C8×D4×C251 | 2 |
| C8×SD16 | 251 |