Finite Group DatabasebetaFinite Group DatabasebetaOrder 29056.
492 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 181 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. #28409509 | C2 | semidirect |
| 4. #28409129 | C2 | semidirect |
| 5. #28409123 | C2 | semidirect |
| 6. #28409068 | C2 | semidirect |
| 7. #28409042 | C2 | semidirect |
| 8. #28408990 | C2 | semidirect |
| 11. C2×#16813872 | C4 | semidirect |
| 16. #20300253 | C22 | semidirect |
| 23. #20300221 | C22 | semidirect |
| 24. #20300219 | C22 | semidirect |
| 25. #20300213 | C22 | semidirect |
| 26. #20300198 | C22 | semidirect |
| 27. C8×Dic227 | C22 | semidirect |
| 34. C2×Dic454 | C2×C4 | semidirect |
| 38. #16813872 | C2×C4 | semidirect |
| 39. #16813872 | C2×C4 | semidirect |
| 40. C2×C227⋊C8 | C2×C4 | semidirect |
| 103. C227 | #2949 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#16813872 | 2 |
| #28409509 | 2 |
| #28409507 | 2 |
| #28409129 | 2 |
| #28409123 | 2 |
| #28409068 | 2 |
| #28409042 | 2 |
| #28408990 | 2 |
| #418×C227 | 2 |
| #2949 | 227 |