Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
212 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 212 conjugacy classes of subgroups — too many to draw. Only its 53 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 |
|---|---|---|
| 3. #30631972 | C2 | semidirect |
| 4. #30631898 | C2 | semidirect |
| 6. #30631419 | C2 | semidirect |
| 7. Q8⋊C8×C251 | C2 | semidirect |
| 90. C251 | #1640 | semidirect |
| 98. Q8⋊C8 | D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30632422 | 2 |
| #30632034 | 2 |
| #30631972 | 2 |
| #30631898 | 2 |
| #30631430 | 2 |
| #30631419 | 2 |
| Q8⋊C8×C251 | 2 |
| #1640 | 251 |