Finite Group DatabasebetaFinite Group DatabasebetaOrder 29248.
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. #28410597 | C2 | semidirect |
| 2. #28410578 | C2 | semidirect |
| 3. #28410576 | C2 | semidirect |
| 4. #28410574 | C2 | semidirect |
| 5. #28410571 | C2 | semidirect |
| 6. D8×D457 | C2 | semidirect |
| 7. #28410558 | C2 | semidirect |
| 8. C2×D8×C457 | C2 | semidirect |
| 10. #20300741 | C22 | semidirect |
| 12. #20300740 | C22 | semidirect |
| 15. D4×D457 | C22 | semidirect |
| 16. Dic1828 | C22 | semidirect |
| 17. #20300730 | C22 | semidirect |
| 18. #20300729 | C22 | semidirect |
| 19. D3656 | C22 | semidirect |
| 20. #20300726 | C22 | semidirect |
| 21. #20300725 | C22 | semidirect |
| 22. #20300724 | C22 | semidirect |
| 23. C8×D457 | C22 | semidirect |
| 24. C2×D4×C457 | C22 | semidirect |
| 25. D8×C457 | C22 | semidirect |
| 26. D8×C457 | C22 | semidirect |
| 27. C2×C8×C457 | C22 | semidirect |
| 62. C457 | #576 | semidirect |
| 70. C2×D8 | D457 | semidirect |
| 79. C2×D4 | C2×D457 | semidirect |
| 85. D8 | C2×D457 | semidirect |
| 86. D8 | C2×D457 | semidirect |
| 90. C2×C8 | C2×D457 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #28410597 | 2 |
| #28410578 | 2 |
| #28410576 | 2 |
| #28410574 | 2 |
| #28410571 | 2 |
| D8×D457 | 2 |
| #28410558 | 2 |
| C2×D8×C457 | 2 |
| #576 | 457 |