Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
552 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 101 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. C2×#22548642 | C2 | semidirect |
| 3. C2×#22548641 | C2 | semidirect |
| 4. #30631686 | C2 | semidirect |
| 5. C2×#22548633 | C2 | semidirect |
| 6. #30631592 | C2 | semidirect |
| 7. #417×C251 | C2 | semidirect |
| 11. #22548762 | C4 | semidirect |
| 154. C251 | #1793 | semidirect |
| 160. #417 | D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22548762 | 2 |
| C2×#22548642 | 2 |
| C2×#22548641 | 2 |
| #30631686 | 2 |
| C2×#22548633 | 2 |
| #30631592 | 2 |
| #417×C251 | 2 |
| #1793 | 251 |