Finite Group DatabasebetaFinite Group DatabasebetaOrder 29056.
310 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 310 conjugacy classes of subgroups — too many to draw. Only its 89 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. #28409041 | C2 | semidirect |
| 5. #28408802 | C2 | semidirect |
| 6. #28408788 | C2 | semidirect |
| 7. #519×C227 | C2 | semidirect |
| 11. C2×#16813874 | C4 | semidirect |
| 12. C2×#16813871 | C4 | semidirect |
| 109. C227 | #1905 | semidirect |
| 112. #519 | D227 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20300319 | 2 |
| #28409050 | 2 |
| #28409041 | 2 |
| #28409005 | 2 |
| #28408802 | 2 |
| #28408788 | 2 |
| #519×C227 | 2 |
| #1905 | 227 |