Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
342 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 342 conjugacy classes of subgroups — too many to draw. Only its 125 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. #30632085 | C2 | semidirect |
| 4. #30632029 | C2 | semidirect |
| 5. #30632018 | C2 | semidirect |
| 6. #30631983 | C2 | semidirect |
| 7. #30631973 | C2 | semidirect |
| 8. #30631945 | C2 | semidirect |
| 9. C4×Dic1004 | C2 | semidirect |
| 10. #30631729 | C2 | semidirect |
| 116. C251 | #3356 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30632407 | 2 |
| #30632394 | 2 |
| #30632085 | 2 |
| #30632029 | 2 |
| #30632018 | 2 |
| #30631983 | 2 |
| #30631973 | 2 |
| #30631945 | 2 |
| C4×Dic1004 | 2 |
| #30631729 | 2 |
| #436×C251 | 2 |
| #3356 | 251 |