Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
256 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 67 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. #30631501 | C2 | semidirect |
| 5. #30631500 | C2 | semidirect |
| 6. #30631499 | C2 | semidirect |
| 7. #361×C251 | C2 | semidirect |
| 17. #22548655 | C22 | semidirect |
| 20. #22548651 | C22 | semidirect |
| 23. M32×C251 | C22 | semidirect |
| 24. #108×C251 | C22 | semidirect |
| 95. D251 | #361 | direct (N × H) |
| 96. C251 | C2×#361 | semidirect |
| 104. #361 | D251 | direct (N × H) |
| 117. M32 | C2×D251 | semidirect |
| 121. #108 | C2×D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D8×D251 | 2 |
| M32×D251 | 2 |
| #108×D251 | 2 |
| #30631501 | 2 |
| #30631500 | 2 |
| #30631499 | 2 |
| #361×C251 | 2 |
| C2×#361 | 251 |