Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
324 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 79 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. #30632453 | C2 | semidirect |
| 3. #30631703 | C2 | semidirect |
| 4. #30631692 | C2 | semidirect |
| 5. #30631459 | C2 | semidirect |
| 6. C251⋊#338 | C2 | semidirect |
| 7. C2×#100×C251 | C2 | semidirect |
| 11. C2×#16860798 | C4 | semidirect |
| 12. C2×#16860795 | C4 | semidirect |
| 112. C251 | #1903 | semidirect |
| 118. C2×#100 | D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22548741 | 2 |
| #30632453 | 2 |
| #30631703 | 2 |
| #30631692 | 2 |
| #30631459 | 2 |
| C251⋊#338 | 2 |
| C2×#100×C251 | 2 |
| #1903 | 251 |