Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
224 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 77 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. #30632092 | C2 | semidirect |
| 3. #30632060 | C2 | semidirect |
| 4. #30632034 | C2 | semidirect |
| 5. C82×C251 | C2 | semidirect |
| 37. C8×C251 | D8 | semidirect |
| 38. C8×C251 | SD16 | semidirect |
| 51. C251 | #1706 | semidirect |
| 57. C82 | D251 | semidirect |
| 89. C8 | D2008 | semidirect |
| 90. C8 | #16860799 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30632092 | 2 |
| #30632064 | 2 |
| #30632060 | 2 |
| #30632034 | 2 |
| C82×C251 | 2 |
| #1706 | 251 |