Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
256 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 63 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. #30631741 | C2 | semidirect |
| 3. #30631737 | C2 | semidirect |
| 4. #30631411 | C2 | semidirect |
| 5. #30631410 | C2 | semidirect |
| 6. #30631410 | C2 | semidirect |
| 7. #323×C251 | C2 | semidirect |
| 119. C251 | #1469 | semidirect |
| 127. #323 | D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22548701 | 2 |
| #30631741 | 2 |
| #30631737 | 2 |
| #30631411 | 2 |
| #30631410 | 2 |
| #323×C251 | 2 |
| #1469 | 251 |