Finite Group DatabasebetaFinite Group DatabasebetaOrder 29056.
312 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 312 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 |
| 5. C4×Dic227⋊C4 | C2 | semidirect |
| 6. #28408791 | C2 | semidirect |
| 7. #339×C227 | C2 | semidirect |
| 10. #20300253 | C4 | semidirect |
| 11. #20300253 | C4 | semidirect |
| 12. #20300250 | C4 | semidirect |
| 13. #20300250 | C4 | semidirect |
| 71. Dic454 | C4⋊C4 | semidirect |
| 73. D908 | C4⋊C4 | semidirect |
| 124. Dic227 | #104 | semidirect |
| 131. C227 | #1806 | semidirect |
| 139. #339 | D227 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #28409500 | 2 |
| #28409055 | 2 |
| C2×#20300216 | 2 |
| C2×#20300214 | 2 |
| C4×Dic227⋊C4 | 2 |
| #28408791 | 2 |
| #339×C227 | 2 |
| #1806 | 227 |