Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
174 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 174 conjugacy classes of subgroups — too many to draw. Only its 59 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. D8×Dic251 | C2 | semidirect |
| 3. #30631769 | C2 | semidirect |
| 4. #30631512 | C2 | semidirect |
| 5. #30631489 | C2 | semidirect |
| 6. C16×Dic251 | C2 | semidirect |
| 7. #357×C251 | C2 | semidirect |
| 11. #22548656 | C4 | semidirect |
| 24. D2008 | C2×C4 | semidirect |
| 30. C251⋊C16 | C2×C4 | semidirect |
| 33. D8×C251 | C2×C4 | semidirect |
| 65. Dic251 | D16 | semidirect |
| 71. C251 | C4×D16 | semidirect |
| 78. #357 | D251 | semidirect |
| 99. D8 | C4×D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22548656 | 2 |
| D8×Dic251 | 2 |
| #30631769 | 2 |
| #30631512 | 2 |
| #30631489 | 2 |
| C16×Dic251 | 2 |
| #357×C251 | 2 |
| C4×D16 | 251 |