Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
408 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 408 conjugacy classes of subgroups — too many to draw. Only its 115 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 |
|---|---|---|
| 1. #31774445 | C2 | semidirect |
| 2. #31774432 | C2 | semidirect |
| 3. #31774307 | C2 | semidirect |
| 4. #31774284 | C2 | semidirect |
| 5. #31774257 | C2 | semidirect |
| 6. #31774149 | C2 | semidirect |
| 7. #31774142 | C2 | semidirect |
| 8. #31773988 | C2 | semidirect |
| 9. #31773977 | C2 | semidirect |
| 10. #31773849 | C2 | semidirect |
| 11. #490×C271 | C2 | semidirect |
| 99. C271⋊C8 | #41 | semidirect |
| 137. C271 | #3171 | semidirect |
| 143. #490 | D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774445 | 2 |
| #31774432 | 2 |
| #31774307 | 2 |
| #31774284 | 2 |
| #31774257 | 2 |
| #31774149 | 2 |
| #31774142 | 2 |
| #31773988 | 2 |
| #31773977 | 2 |
| #31773849 | 2 |
| #490×C271 | 2 |
| #3171 | 271 |