Finite Group DatabasebetaFinite Group DatabasebetaOrder 30656.
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. #29506427 | C2 | semidirect |
| 2. #29506408 | C2 | semidirect |
| 3. #29506406 | C2 | semidirect |
| 4. #29506404 | C2 | semidirect |
| 5. #29506401 | C2 | semidirect |
| 6. D8×D479 | C2 | semidirect |
| 7. #29506388 | C2 | semidirect |
| 8. C2×D8×C479 | C2 | semidirect |
| 10. #21440162 | C22 | semidirect |
| 12. #21440161 | C22 | semidirect |
| 15. D4×D479 | C22 | semidirect |
| 16. Dic1916 | C22 | semidirect |
| 17. #21440151 | C22 | semidirect |
| 18. #21440150 | C22 | semidirect |
| 19. D3832 | C22 | semidirect |
| 20. #21440147 | C22 | semidirect |
| 21. #21440146 | C22 | semidirect |
| 22. #21440145 | C22 | semidirect |
| 23. C8×D479 | C22 | semidirect |
| 24. C2×D4×C479 | C22 | semidirect |
| 25. D8×C479 | C22 | semidirect |
| 26. D8×C479 | C22 | semidirect |
| 27. C2×C8×C479 | C22 | semidirect |
| 62. C479 | #576 | semidirect |
| 70. C2×D8 | D479 | semidirect |
| 79. C2×D4 | C2×D479 | semidirect |
| 85. D8 | C2×D479 | semidirect |
| 86. D8 | C2×D479 | semidirect |
| 90. C2×C8 | C2×D479 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #29506427 | 2 |
| #29506408 | 2 |
| #29506406 | 2 |
| #29506404 | 2 |
| #29506401 | 2 |
| D8×D479 | 2 |
| #29506388 | 2 |
| C2×D8×C479 | 2 |
| #576 | 479 |