Finite Group DatabasebetaFinite Group DatabasebetaOrder 29056.
458 conjugacy classes of subgroups; only the 177 normal subgroups are shown.
This group has 458 conjugacy classes of subgroups — too many to draw. Only its 177 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. #28409798 | C2 | semidirect |
| 3. #28409153 | C2 | semidirect |
| 4. #28409148 | C2 | semidirect |
| 5. C2×#20300214 | C2 | semidirect |
| 6. M16×Dic227 | C2 | semidirect |
| 7. #430×C227 | C2 | semidirect |
| 9. #20300321 | C4 | semidirect |
| 10. #20300316 | C4 | semidirect |
| 12. #20300296 | C22 | semidirect |
| 17. #20300214 | C22 | semidirect |
| 18. #20300214 | C22 | semidirect |
| 19. #20300198 | C22 | semidirect |
| 20. C8×Dic227 | C22 | semidirect |
| 23. #108×C227 | C22 | semidirect |
| 33. Dic908 | C2×C4 | semidirect |
| 34. #16813873 | C2×C4 | semidirect |
| 35. D1816 | C2×C4 | semidirect |
| 85. C227 | #2956 | semidirect |
| 91. #430 | D227 | semidirect |
| 105. #108 | C2×D227 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #28409832 | 2 |
| #28409798 | 2 |
| #28409153 | 2 |
| #28409148 | 2 |
| C2×#20300214 | 2 |
| M16×Dic227 | 2 |
| #430×C227 | 2 |
| #2956 | 227 |