Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
426 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 426 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. #30632358 | C2 | semidirect |
| 2. #30632352 | C2 | semidirect |
| 3. #30632035 | C2 | semidirect |
| 4. #30632032 | C2 | semidirect |
| 5. #30631966 | C2 | semidirect |
| 6. #30631883 | C2 | semidirect |
| 7. #30631881 | C2 | semidirect |
| 8. #30631811 | C2 | semidirect |
| 9. #30631769 | C2 | semidirect |
| 10. C4×#16860795 | C2 | semidirect |
| 11. #474×C251 | C2 | semidirect |
| 78. Dic502 | D8 | semidirect |
| 84. D1004 | #41 | semidirect |
| 131. C251 | #3358 | semidirect |
| 138. #474 | D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30632358 | 2 |
| #30632352 | 2 |
| #30632035 | 2 |
| #30632032 | 2 |
| #30631966 | 2 |
| #30631883 | 2 |
| #30631881 | 2 |
| #30631811 | 2 |
| #30631769 | 2 |
| C4×#16860795 | 2 |
| #474×C251 | 2 |
| #3358 | 251 |