Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
358 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 358 conjugacy classes of subgroups — too many to draw. Only its 121 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 |
|---|---|---|
| 4. #30631995 | C2 | semidirect |
| 5. #30631898 | C2 | semidirect |
| 7. #30631795 | C2 | semidirect |
| 8. C4×Dic1004 | C2 | semidirect |
| 95. C251 | #3127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30632299 | 2 |
| #30632164 | 2 |
| #30632029 | 2 |
| #30631995 | 2 |
| #30631898 | 2 |
| #30631845 | 2 |
| #30631795 | 2 |
| C4×Dic1004 | 2 |
| #433×C251 | 2 |
| #3127 | 251 |