Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
340 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 340 conjugacy classes of subgroups — too many to draw. Only its 137 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. #30632095 | C2 | semidirect |
| 3. #30632093 | C2 | semidirect |
| 4. #30632091 | C2 | semidirect |
| 5. #30632089 | C2 | semidirect |
| 6. #30632088 | C2 | semidirect |
| 11. #500×C251 | C2 | semidirect |
| 42. #16860793 | Q8 | semidirect |
| 45. C8×D251 | Q8 | semidirect |
| 107. C251 | #3164 | semidirect |
| 113. #500 | D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30632314 | 2 |
| #30632095 | 2 |
| #30632093 | 2 |
| #30632091 | 2 |
| #30632089 | 2 |
| #30632088 | 2 |
| #30631728 | 2 |
| #30631724 | 2 |
| #107×D251 | 2 |
| #30631641 | 2 |
| #500×C251 | 2 |
| #3164 | 251 |