Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
396 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 123 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. #30632397 | C2 | semidirect |
| 2. #30632051 | C2 | semidirect |
| 3. #30632033 | C2 | semidirect |
| 4. #30631987 | C2 | semidirect |
| 5. #30631977 | C2 | semidirect |
| 6. #30631879 | C2 | semidirect |
| 7. #30631879 | C2 | semidirect |
| 8. #30631818 | C2 | semidirect |
| 9. #30631797 | C2 | semidirect |
| 10. C4×#16860795 | C2 | semidirect |
| 11. #550×C251 | C2 | semidirect |
| 77. D1004 | #41 | semidirect |
| 129. C251 | #3366 | semidirect |
| 132. #550 | D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30632397 | 2 |
| #30632051 | 2 |
| #30632033 | 2 |
| #30631987 | 2 |
| #30631977 | 2 |
| #30631879 | 2 |
| #30631818 | 2 |
| #30631797 | 2 |
| C4×#16860795 | 2 |
| #550×C251 | 2 |
| #3366 | 251 |