Finite Group DatabasebetaFinite Group DatabasebetaOrder 29056.
324 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 79 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. #28409798 | C2 | semidirect |
| 3. #28409048 | C2 | semidirect |
| 4. #28409038 | C2 | semidirect |
| 5. C2×#20300204 | C2 | semidirect |
| 6. #28408803 | C2 | semidirect |
| 7. #338×C227 | C2 | semidirect |
| 12. C2×#16813873 | C4 | semidirect |
| 13. C2×D1816 | C4 | semidirect |
| 112. C227 | #1903 | semidirect |
| 120. #338 | D227 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20300316 | 2 |
| #28409798 | 2 |
| #28409048 | 2 |
| #28409038 | 2 |
| C2×#20300204 | 2 |
| #28408803 | 2 |
| #338×C227 | 2 |
| #1903 | 227 |