Finite Group DatabasebetaFinite Group DatabasebetaOrder 29056.
360 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 87 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. #28409055 | C2 | semidirect |
| 3. C2×#20300216 | C2 | semidirect |
| 4. C2×#20300215 | C2 | semidirect |
| 5. C2×#20300214 | C2 | semidirect |
| 6. C42×Dic227 | C2 | semidirect |
| 7. C2×#104×C227 | C2 | semidirect |
| 10. #20300286 | C4 | semidirect |
| 11. #20300284 | C4 | semidirect |
| 12. #20300277 | C4 | semidirect |
| 13. #20300275 | C4 | semidirect |
| 49. C4×Dic227 | D4 | semidirect |
| 64. C42×C227 | D4 | semidirect |
| 119. Dic227 | #104 | semidirect |
| 126. C227 | #1962 | semidirect |
| 133. C2×#104 | D227 | semidirect |
| 191. C42 | C22⋊D227 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #28409578 | 2 |
| #28409055 | 2 |
| C2×#20300216 | 2 |
| C2×#20300215 | 2 |
| C2×#20300214 | 2 |
| C42×Dic227 | 2 |
| C2×#104×C227 | 2 |
| #1962 | 227 |