Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
396 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 115 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. #30632398 | C2 | semidirect |
| 2. #30632358 | C2 | semidirect |
| 3. #30632050 | C2 | semidirect |
| 4. #30632035 | C2 | semidirect |
| 5. #30631986 | C2 | semidirect |
| 6. #30631883 | C2 | semidirect |
| 7. #30631881 | C2 | semidirect |
| 8. #30631814 | C2 | semidirect |
| 9. #30631798 | C2 | semidirect |
| 10. C4×#16860795 | C2 | semidirect |
| 11. #476×C251 | C2 | semidirect |
| 82. D1004 | #41 | semidirect |
| 129. C251 | #3366 | semidirect |
| 136. #476 | D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30632398 | 2 |
| #30632358 | 2 |
| #30632050 | 2 |
| #30632035 | 2 |
| #30631986 | 2 |
| #30631883 | 2 |
| #30631881 | 2 |
| #30631814 | 2 |
| #30631798 | 2 |
| C4×#16860795 | 2 |
| #476×C251 | 2 |
| #3366 | 251 |