Finite Group DatabasebetaFinite Group DatabasebetaOrder 29056.
292 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 117 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 |
|---|---|---|
| 3. #28408990 | C2 | semidirect |
| 4. C2×#20300199 | C2 | semidirect |
| 5. #28408796 | C2 | semidirect |
| 6. #28408792 | C2 | semidirect |
| 9. #20300295 | C4 | semidirect |
| 16. #20300212 | C4 | semidirect |
| 17. #20300209 | C4 | semidirect |
| 24. #104×C227 | C4 | semidirect |
| 98. C227 | #1765 | semidirect |
| 118. #104 | Dic227 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20300295 | 2 |
| #28409028 | 2 |
| #28408990 | 2 |
| C2×#20300199 | 2 |
| #28408796 | 2 |
| #28408792 | 2 |
| C2×#104×C227 | 2 |
| #1765 | 227 |