Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
336 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 336 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 |
|---|---|---|
| 2. #30632089 | C2 | semidirect |
| 3. #30632029 | C2 | semidirect |
| 4. #30632023 | C2 | semidirect |
| 5. #30631995 | C2 | semidirect |
| 6. #30631945 | C2 | semidirect |
| 7. C4×Dic1004 | C2 | semidirect |
| 8. #30631729 | C2 | semidirect |
| 96. C251 | #3352 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30632377 | 2 |
| #30632089 | 2 |
| #30632029 | 2 |
| #30632023 | 2 |
| #30631995 | 2 |
| #30631945 | 2 |
| C4×Dic1004 | 2 |
| #30631729 | 2 |
| #436×C251 | 2 |
| #3352 | 251 |