Finite Group DatabasebetaFinite Group DatabasebetaOrder 29056.
564 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 149 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. C22×#16813871 | C2 | semidirect |
| 3. C2×#20300277 | C2 | semidirect |
| 4. C2×#20300250 | C2 | semidirect |
| 5. #28409250 | C2 | direct (N × H) |
| 6. C2×Dic227⋊C8 | C2 | semidirect |
| 7. C2×#20300208 | C2 | semidirect |
| 8. C2×#103×C227 | C2 | semidirect |
| 13. C2×#16813871 | C22 | semidirect |
| 18. #20300277 | C22 | semidirect |
| 20. #20300250 | C22 | semidirect |
| 25. Dic227⋊C8 | C22 | semidirect |
| 26. #20300208 | C22 | semidirect |
| 30. #103×C227 | C22 | semidirect |
| 117. C2×C227 | #463 | semidirect |
| 123. C227 | C2×#463 | semidirect |
| 131. C2×#103 | D227 | semidirect |
| 153. #103 | C2×D227 | semidirect |
| 243. C2 | #28409250 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#16813871 | 2 |
| C22×D1816 | 2 |
| C2×#20300277 | 2 |
| C2×#20300250 | 2 |
| #28409250 | 2 |
| C2×Dic227⋊C8 | 2 |
| C2×#20300208 | 2 |
| C2×#103×C227 | 2 |
| C2×#463 | 227 |