Finite Group DatabasebetaFinite Group DatabasebetaOrder 32192.
258 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 107 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. #30632910 | C2 | semidirect |
| 2. #30632895 | C2 | semidirect |
| 3. #30632889 | C2 | semidirect |
| 4. #30632884 | C2 | semidirect |
| 5. C2×#22548870 | C2 | semidirect |
| 6. #30632871 | C2 | semidirect |
| 7. 2−1+4×C503 | C2 | semidirect |
| 12. #22548873 | C22 | semidirect |
| 13. #22548871 | C22 | semidirect |
| 14. #22548870 | C22 | semidirect |
| 15. #22548870 | C22 | semidirect |
| 16. #22548868 | C22 | semidirect |
| 17. #22548867 | C22 | semidirect |
| 18. C2×C503⋊C8 | C22 | semidirect |
| 21. #41×C503 | C22 | semidirect |
| 23. C2×Q8×C503 | C22 | semidirect |
| 53. C503 | #577 | semidirect |
| 55. 2−1+4 | D503 | semidirect |
| 66. #41 | C2×D503 | semidirect |
| 68. C2×Q8 | C2×D503 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30632910 | 2 |
| #30632895 | 2 |
| #30632889 | 2 |
| #30632884 | 2 |
| C2×#22548870 | 2 |
| #30632871 | 2 |
| 2−1+4×C503 | 2 |
| #577 | 503 |