Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
386 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 386 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. #30632402 | C2 | semidirect |
| 2. #30632340 | C2 | semidirect |
| 3. #30632083 | C2 | semidirect |
| 4. #30632014 | C2 | semidirect |
| 5. #30632004 | C2 | semidirect |
| 6. #30631978 | C2 | semidirect |
| 7. #30631939 | C2 | semidirect |
| 8. C4×#16860795 | C2 | semidirect |
| 9. #30631764 | C2 | semidirect |
| 10. #30631728 | C2 | semidirect |
| 11. #474×C251 | C2 | semidirect |
| 90. C251⋊C8 | #41 | semidirect |
| 127. C251 | #3354 | semidirect |
| 135. #474 | D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30632402 | 2 |
| #30632340 | 2 |
| #30632083 | 2 |
| #30632014 | 2 |
| #30632004 | 2 |
| #30631978 | 2 |
| #30631939 | 2 |
| C4×#16860795 | 2 |
| #30631764 | 2 |
| #30631728 | 2 |
| #474×C251 | 2 |
| #3354 | 251 |