Finite Group DatabasebetaFinite Group DatabasebetaOrder 29248.
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. #28410599 | C2 | semidirect |
| 2. #28410598 | C2 | semidirect |
| 3. #28410585 | C2 | semidirect |
| 4. #28410580 | C2 | semidirect |
| 5. #28410574 | C2 | semidirect |
| 6. C2×#20300730 | C2 | semidirect |
| 7. #131×C457 | C2 | semidirect |
| 10. #20300741 | C22 | semidirect |
| 12. C2×Dic914 | C22 | semidirect |
| 16. Dic1828 | C22 | semidirect |
| 17. #20300730 | C22 | semidirect |
| 18. #20300730 | C22 | semidirect |
| 19. #20300730 | C22 | semidirect |
| 20. D3656 | C22 | semidirect |
| 22. M16×C457 | C22 | semidirect |
| 23. C2×C8×C457 | C22 | semidirect |
| 53. C457 | #577 | semidirect |
| 61. #131 | D457 | semidirect |
| 76. M16 | C2×D457 | semidirect |
| 77. C2×C8 | C2×D457 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #28410599 | 2 |
| #28410598 | 2 |
| #28410585 | 2 |
| #28410580 | 2 |
| #28410574 | 2 |
| C2×#20300730 | 2 |
| #131×C457 | 2 |
| #577 | 457 |