Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
388 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 388 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. #30632038 | C2 | semidirect |
| 4. #30632024 | C2 | semidirect |
| 5. #30631982 | C2 | semidirect |
| 6. #30631927 | C2 | semidirect |
| 7. #30631897 | C2 | semidirect |
| 8. #30631841 | C2 | semidirect |
| 10. #103×D251 | C2 | semidirect |
| 11. C4×Q16×C251 | C2 | semidirect |
| 81. D1004 | Q16 | semidirect |
| 122. C251 | #3299 | semidirect |
| 132. C4×Q16 | D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30632397 | 2 |
| Q8×D1004 | 2 |
| #30632038 | 2 |
| #30632024 | 2 |
| #30631982 | 2 |
| #30631927 | 2 |
| #30631897 | 2 |
| #30631841 | 2 |
| C8×D1004 | 2 |
| #103×D251 | 2 |
| C4×Q16×C251 | 2 |
| #3299 | 251 |