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. #28410598 | C2 | semidirect |
| 2. #28410583 | C2 | semidirect |
| 3. #28410577 | C2 | semidirect |
| 4. #28410572 | C2 | semidirect |
| 5. C2×#20300728 | C2 | semidirect |
| 6. #28410559 | C2 | semidirect |
| 7. 2−1+4×C457 | C2 | semidirect |
| 12. #20300731 | C22 | semidirect |
| 13. #20300729 | C22 | semidirect |
| 14. #20300728 | C22 | semidirect |
| 15. #20300728 | C22 | semidirect |
| 16. #20300726 | C22 | semidirect |
| 17. #20300725 | C22 | semidirect |
| 18. C2×#16814532 | C22 | semidirect |
| 21. #41×C457 | C22 | semidirect |
| 23. C2×Q8×C457 | C22 | semidirect |
| 53. C457 | #577 | semidirect |
| 55. 2−1+4 | D457 | semidirect |
| 66. #41 | C2×D457 | semidirect |
| 68. C2×Q8 | C2×D457 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #28410598 | 2 |
| #28410583 | 2 |
| #28410577 | 2 |
| #28410572 | 2 |
| C2×#20300728 | 2 |
| #28410559 | 2 |
| 2−1+4×C457 | 2 |
| #577 | 457 |