Finite Group DatabasebetaFinite Group DatabasebetaOrder 29056.
222 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 222 conjugacy classes of subgroups — too many to draw. Only its 75 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 |
|---|---|---|
| 4. C2×#20300198 | C2 | semidirect |
| 5. #28408796 | C2 | semidirect |
| 6. #28408791 | C2 | semidirect |
| 7. #424×C227 | C2 | semidirect |
| 13. #20300211 | C4 | semidirect |
| 14. #20300208 | C4 | semidirect |
| 90. C227 | #1938 | semidirect |
| 92. #424 | D227 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20300214 | 2 |
| #28409026 | 2 |
| #28408998 | 2 |
| C2×#20300198 | 2 |
| #28408796 | 2 |
| #28408791 | 2 |
| #424×C227 | 2 |
| #1938 | 227 |