Finite Group DatabasebetaFinite Group DatabasebetaOrder 32192.
106 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 106 conjugacy classes of subgroups — too many to draw. Only its 45 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 |
|---|---|---|
| 2. #30632872 | C2 | semidirect |
| 3. #30632871 | C2 | semidirect |
| 4. #30632799 | C2 | semidirect |
| 5. #30632792 | C2 | semidirect |
| 6. C4×C503⋊C8 | C2 | semidirect |
| 7. #104×C503 | C2 | semidirect |
| 9. #22548873 | C4 | semidirect |
| 10. #22548871 | C4 | semidirect |
| 11. #22548870 | C4 | semidirect |
| 12. #22548868 | C4 | semidirect |
| 51. C503 | #443 | semidirect |
| 58. #104 | D503 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30632884 | 2 |
| #30632872 | 2 |
| #30632871 | 2 |
| #30632799 | 2 |
| #30632792 | 2 |
| C4×C503⋊C8 | 2 |
| #104×C503 | 2 |
| #443 | 503 |