Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
386 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 386 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. #30632407 | C2 | semidirect |
| 3. #30632038 | C2 | semidirect |
| 4. #30632029 | C2 | semidirect |
| 5. #30631968 | C2 | semidirect |
| 6. #30631928 | C2 | semidirect |
| 7. #30631898 | C2 | semidirect |
| 8. #30631851 | C2 | semidirect |
| 9. C4×#16860799 | C2 | semidirect |
| 10. #30631684 | C2 | semidirect |
| 11. C8×D4×C251 | C2 | semidirect |
| 125. C251 | #3302 | semidirect |
| 136. C8×D4 | D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30632407 | 2 |
| #30632342 | 2 |
| #30632038 | 2 |
| #30632029 | 2 |
| #30631968 | 2 |
| #30631928 | 2 |
| #30631898 | 2 |
| #30631851 | 2 |
| C4×#16860799 | 2 |
| #30631684 | 2 |
| C8×D4×C251 | 2 |
| #3302 | 251 |