Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
388 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 139 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. #30632023 | C2 | semidirect |
| 5. #30631983 | C2 | semidirect |
| 6. #30631928 | C2 | semidirect |
| 7. #30631898 | C2 | semidirect |
| 8. #30631845 | C2 | semidirect |
| 9. C4×Dic1004 | C2 | semidirect |
| 10. C2×#22548640 | C2 | semidirect |
| 93. D4×C251 | Q16 | semidirect |
| 122. C251 | #3299 | semidirect |
| 208. D4 | Dic1004 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30632394 | 2 |
| D4×Dic502 | 2 |
| #30632038 | 2 |
| #30632023 | 2 |
| #30631983 | 2 |
| #30631928 | 2 |
| #30631898 | 2 |
| #30631845 | 2 |
| C4×Dic1004 | 2 |
| C2×#22548640 | 2 |
| C8×D4×C251 | 2 |
| #3299 | 251 |