Finite Group DatabasebetaFinite Group DatabasebetaOrder 29056.
484 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 135 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. C2×#20300321 | C2 | semidirect |
| 2. C2×#20300318 | C2 | semidirect |
| 4. C2×#20300253 | C2 | semidirect |
| 5. #28409257 | C2 | semidirect |
| 6. #28409253 | C2 | semidirect |
| 7. #28409241 | C2 | semidirect |
| 8. #28409231 | C2 | semidirect |
| 9. #28409055 | C2 | semidirect |
| 10. #28409031 | C2 | semidirect |
| 11. #417×C227 | C2 | semidirect |
| 49. C2×Dic454 | D4 | semidirect |
| 150. Dic227 | #137 | semidirect |
| 157. C227 | #3037 | semidirect |
| 169. #417 | D227 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20300321 | 2 |
| C2×#20300318 | 2 |
| #28409578 | 2 |
| C2×#20300253 | 2 |
| #28409257 | 2 |
| #28409253 | 2 |
| #28409241 | 2 |
| #28409231 | 2 |
| #28409055 | 2 |
| #28409031 | 2 |
| #417×C227 | 2 |
| #3037 | 227 |