Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
368 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 129 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. #30632091 | C2 | semidirect |
| 3. #30632065 | C2 | semidirect |
| 4. #30632036 | C2 | semidirect |
| 8. C4×Dic1004 | C2 | semidirect |
| 9. C4×#16860800 | C2 | semidirect |
| 11. C4×Q16×C251 | C2 | semidirect |
| 83. C4×D251 | Q16 | semidirect |
| 114. C251 | #3170 | semidirect |
| 125. C4×Q16 | D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30632241 | 2 |
| #30632091 | 2 |
| #30632065 | 2 |
| #30632036 | 2 |
| #30631929 | 2 |
| #30631927 | 2 |
| #30631925 | 2 |
| C4×Dic1004 | 2 |
| C4×#16860800 | 2 |
| C4×C8×D251 | 2 |
| C4×Q16×C251 | 2 |
| #3170 | 251 |