Finite Group DatabasebetaFinite Group DatabasebetaOrder 32192.
268 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 268 conjugacy classes of subgroups — too many to draw. Only its 99 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. #30632891 | C2 | semidirect |
| 3. #30632889 | C2 | semidirect |
| 4. #30632887 | C2 | semidirect |
| 5. C2×D4024 | C2 | semidirect |
| 6. D8×D503 | C2 | semidirect |
| 7. #30632870 | C2 | semidirect |
| 8. #135×C503 | C2 | semidirect |
| 9. #22548884 | C22 | semidirect |
| 13. C2×D2012 | C22 | semidirect |
| 15. D4×D503 | C22 | semidirect |
| 16. #22548870 | C22 | semidirect |
| 17. D4024 | C22 | semidirect |
| 18. D4024 | C22 | semidirect |
| 19. #22548868 | C22 | semidirect |
| 20. #22548867 | C22 | semidirect |
| 21. #22548866 | C22 | semidirect |
| 22. C8×D503 | C22 | semidirect |
| 23. #41×C503 | C22 | semidirect |
| 24. Q16×C503 | C22 | semidirect |
| 25. SD16×C503 | C22 | semidirect |
| 26. D8×C503 | C22 | semidirect |
| 27. C2×C8×C503 | C22 | semidirect |
| 62. C503 | #576 | semidirect |
| 68. #135 | D503 | semidirect |
| 75. #41 | C2×D503 | semidirect |
| 80. Q16 | C2×D503 | semidirect |
| 82. SD16 | C2×D503 | semidirect |
| 86. D8 | C2×D503 | semidirect |
| 90. C2×C8 | C2×D503 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30632910 | 2 |
| #30632891 | 2 |
| #30632889 | 2 |
| #30632887 | 2 |
| C2×D4024 | 2 |
| D8×D503 | 2 |
| #30632870 | 2 |
| #135×C503 | 2 |
| #576 | 503 |