Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
266 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 266 conjugacy classes of subgroups — too many to draw. Only its 57 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 |
|---|---|---|
| 1. C22×D2008 | C2 | semidirect |
| 2. C2×#22548656 | C2 | semidirect |
| 3. #30631487 | C2 | semidirect |
| 4. C22⋊(C251⋊C16) | C2 | semidirect |
| 5. #466×C251 | C2 | semidirect |
| 11. C2×C251⋊C16 | C22 | semidirect |
| 12. C2×D8×C251 | C22 | semidirect |
| 15. #107×C251 | C22 | semidirect |
| 24. D2008 | D4 | semidirect |
| 59. C22×C251 | D16 | semidirect |
| 75. C251 | #2184 | semidirect |
| 79. #466 | D251 | semidirect |
| 86. C2×D8 | C2×D251 | semidirect |
| 91. #107 | C2×D251 | semidirect |
| 139. C22 | #22548656 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D2008 | 2 |
| C2×#22548656 | 2 |
| #30631487 | 2 |
| C22⋊(C251⋊C16) | 2 |
| #466×C251 | 2 |
| #2184 | 251 |