Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
386 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 117 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. #30632403 | C2 | semidirect |
| 2. #30632340 | C2 | semidirect |
| 3. #30632013 | C2 | semidirect |
| 4. #30632007 | C2 | semidirect |
| 5. #30631974 | C2 | semidirect |
| 6. #30631964 | C2 | semidirect |
| 7. #30631941 | C2 | semidirect |
| 8. C4×D2008 | C2 | semidirect |
| 9. #30631766 | C2 | semidirect |
| 10. #30631726 | C2 | semidirect |
| 11. #498×C251 | C2 | semidirect |
| 101. C8×C251 | #41 | semidirect |
| 127. C251 | #3354 | semidirect |
| 131. #498 | D251 | semidirect |
| 229. C8 | #16860811 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30632403 | 2 |
| #30632340 | 2 |
| #30632013 | 2 |
| #30632007 | 2 |
| #30631974 | 2 |
| #30631964 | 2 |
| #30631941 | 2 |
| C4×D2008 | 2 |
| #30631766 | 2 |
| #30631726 | 2 |
| #498×C251 | 2 |
| #3354 | 251 |