Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
220 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 220 conjugacy classes of subgroups — too many to draw. Only its 65 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. M32×D251 | C2 | semidirect |
| 3. #108×D251 | C2 | semidirect |
| 4. #30631503 | C2 | semidirect |
| 5. #30631501 | C2 | semidirect |
| 6. #30631499 | C2 | semidirect |
| 7. #362×C251 | C2 | semidirect |
| 91. C251 | #2148 | semidirect |
| 97. #362 | D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22548738 | 2 |
| M32×D251 | 2 |
| #108×D251 | 2 |
| #30631503 | 2 |
| #30631501 | 2 |
| #30631499 | 2 |
| #362×C251 | 2 |
| #2148 | 251 |