Finite Group DatabasebetaFinite Group DatabasebetaOrder 33472.
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. #30660418 | C2 | semidirect |
| 2. #30660399 | C2 | semidirect |
| 3. #30660397 | C2 | semidirect |
| 4. #30660395 | C2 | semidirect |
| 5. #30660392 | C2 | semidirect |
| 6. D8×D523 | C2 | semidirect |
| 7. #30660379 | C2 | semidirect |
| 8. C2×D8×C523 | C2 | semidirect |
| 10. #22552641 | C22 | semidirect |
| 12. #22552640 | C22 | semidirect |
| 15. D4×D523 | C22 | semidirect |
| 16. Dic2092 | C22 | semidirect |
| 17. #22552630 | C22 | semidirect |
| 18. #22552629 | C22 | semidirect |
| 19. D4184 | C22 | semidirect |
| 20. #22552626 | C22 | semidirect |
| 21. #22552625 | C22 | semidirect |
| 22. #22552624 | C22 | semidirect |
| 23. C8×D523 | C22 | semidirect |
| 24. C2×D4×C523 | C22 | semidirect |
| 25. D8×C523 | C22 | semidirect |
| 26. D8×C523 | C22 | semidirect |
| 27. C2×C8×C523 | C22 | semidirect |
| 62. C523 | #576 | semidirect |
| 70. C2×D8 | D523 | semidirect |
| 79. C2×D4 | C2×D523 | semidirect |
| 85. D8 | C2×D523 | semidirect |
| 86. D8 | C2×D523 | semidirect |
| 90. C2×C8 | C2×D523 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30660418 | 2 |
| #30660399 | 2 |
| #30660397 | 2 |
| #30660395 | 2 |
| #30660392 | 2 |
| D8×D523 | 2 |
| #30660379 | 2 |
| C2×D8×C523 | 2 |
| #576 | 523 |