Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
380 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 380 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. #30632054 | C2 | semidirect |
| 4. #30632039 | C2 | semidirect |
| 5. #30632038 | C2 | semidirect |
| 6. #30632037 | C2 | semidirect |
| 9. #487×C251 | C2 | semidirect |
| 106. C251 | #3139 | semidirect |
| 114. #487 | D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30632242 | 2 |
| C4⋊Q8×D251 | 2 |
| #30632054 | 2 |
| #30632039 | 2 |
| #30632038 | 2 |
| #30632037 | 2 |
| #30631694 | 2 |
| C4×#16860793 | 2 |
| #487×C251 | 2 |
| #3139 | 251 |