Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
224 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 69 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. #30632090 | C2 | semidirect |
| 3. #30632060 | C2 | semidirect |
| 4. #30632035 | C2 | semidirect |
| 5. #30632033 | C2 | semidirect |
| 6. C8×C251⋊C8 | C2 | semidirect |
| 7. #492×C251 | C2 | semidirect |
| 47. C251⋊C8 | SD16 | semidirect |
| 57. C8×C251 | D8 | semidirect |
| 75. C251 | #1706 | semidirect |
| 80. #492 | D251 | semidirect |
| 133. C8 | #16860795 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30632090 | 2 |
| #30632063 | 2 |
| #30632060 | 2 |
| #30632035 | 2 |
| #30632033 | 2 |
| C8×C251⋊C8 | 2 |
| #492×C251 | 2 |
| #1706 | 251 |