Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
368 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 133 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. #30632092 | C2 | semidirect |
| 3. #30632037 | C2 | semidirect |
| 5. Q16×Dic251 | C2 | semidirect |
| 7. #494×C251 | C2 | semidirect |
| 53. C4×D251 | Q16 | semidirect |
| 77. C251 | #3170 | semidirect |
| 81. #494 | D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30632242 | 2 |
| #30632092 | 2 |
| #30632037 | 2 |
| #30631925 | 2 |
| Q16×Dic251 | 2 |
| C4×C8×D251 | 2 |
| #494×C251 | 2 |
| #3170 | 251 |