Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
362 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 121 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. #31774296 | C2 | semidirect |
| 3. #31774271 | C2 | semidirect |
| 4. #31774265 | C2 | semidirect |
| 5. #31774263 | C2 | semidirect |
| 6. #31774145 | C2 | semidirect |
| 7. #31774128 | C2 | semidirect |
| 8. #31773995 | C2 | semidirect |
| 9. C4×#16864641 | C2 | semidirect |
| 10. #31773853 | C2 | semidirect |
| 11. #541×C271 | C2 | semidirect |
| 108. C271 | #3174 | semidirect |
| 110. #541 | D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774502 | 2 |
| #31774296 | 2 |
| #31774271 | 2 |
| #31774265 | 2 |
| #31774263 | 2 |
| #31774145 | 2 |
| #31774128 | 2 |
| #31773995 | 2 |
| C4×#16864641 | 2 |
| #31773853 | 2 |
| #541×C271 | 2 |
| #3174 | 271 |