Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
792 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 792 conjugacy classes of subgroups — too many to draw. Only its 181 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. C23×Dic502 | C2 | semidirect |
| 2. C22×#16860798 | C2 | semidirect |
| 3. #30631825 | C2 | direct (N × H) |
| 4. C2×#22548638 | C2 | semidirect |
| 5. C2×C22⋊(C251⋊C8) | C2 | semidirect |
| 11. C22×Dic502 | C22 | semidirect |
| 14. C2×#16860798 | C22 | semidirect |
| 16. #22548638 | C22 | semidirect |
| 17. C22⋊(C251⋊C8) | C22 | semidirect |
| 31. C2×Dic502 | D4 | semidirect |
| 58. Dic502 | C2×D4 | semidirect |
| 69. C23×C251 | SD16 | semidirect |
| 93. C22×C251 | C2×SD16 | semidirect |
| 103. C2×C251 | #448 | semidirect |
| 107. C251 | C2×#448 | semidirect |
| 169. C23 | #16860798 | semidirect |
| 201. C22 | C2×#16860798 | semidirect |
| 211. C2 | #30631825 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×Dic502 | 2 |
| C22×#16860798 | 2 |
| #30631825 | 2 |
| C2×#22548638 | 2 |
| C2×C22⋊(C251⋊C8) | 2 |
| C2×#121×C251 | 2 |
| C2×#448 | 251 |