Finite Group DatabasebetaFinite Group DatabasebetaOrder 29056.
716 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 716 conjugacy classes of subgroups — too many to draw. Only its 133 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 |
|---|---|---|
| 2. #28409604 | C2 | semidirect |
| 3. #28409223 | C2 | semidirect |
| 4. #28409222 | C2 | semidirect |
| 5. #28409221 | C2 | semidirect |
| 6. #28409004 | C2 | semidirect |
| 7. #458×C227 | C2 | semidirect |
| 14. C22×Dic454 | C22 | semidirect |
| 17. #20300272 | C22 | semidirect |
| 18. #20300271 | C22 | semidirect |
| 19. #20300269 | C22 | semidirect |
| 22. #20300244 | C22 | semidirect |
| 23. #20300203 | C22 | semidirect |
| 24. #20300202 | C22 | semidirect |
| 26. #123×C227 | C22 | semidirect |
| 27. #99×C227 | C22 | semidirect |
| 120. C227 | #3028 | semidirect |
| 127. #458 | D227 | semidirect |
| 142. #123 | C2×D227 | semidirect |
| 148. #99 | C2×D227 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #28409867 | 2 |
| #28409604 | 2 |
| #28409223 | 2 |
| #28409222 | 2 |
| #28409221 | 2 |
| #28409004 | 2 |
| #458×C227 | 2 |
| #3028 | 227 |