Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
142 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 142 conjugacy classes of subgroups — too many to draw. Only its 55 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. #30631514 | C2 | semidirect |
| 3. C4⋊(C251⋊C16) | C2 | semidirect |
| 5. #500×C251 | C2 | semidirect |
| 18. D2008 | Q8 | semidirect |
| 55. C251 | #2226 | semidirect |
| 57. #500 | D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×D2008 | 2 |
| #30631514 | 2 |
| C4⋊(C251⋊C16) | 2 |
| #30631487 | 2 |
| #500×C251 | 2 |
| #2226 | 251 |