Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
408 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 408 conjugacy classes of subgroups — too many to draw. Only its 117 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. #31774613 | C2 | semidirect |
| 2. #31774569 | C2 | semidirect |
| 3. #31774245 | C2 | semidirect |
| 4. #31774224 | C2 | semidirect |
| 5. #31774134 | C2 | semidirect |
| 6. #31774093 | C2 | semidirect |
| 7. #31774045 | C2 | semidirect |
| 8. C4×#16864641 | C2 | semidirect |
| 9. #31773962 | C2 | semidirect |
| 10. #31773892 | C2 | semidirect |
| 11. #477×C271 | C2 | semidirect |
| 132. C271 | #3305 | semidirect |
| 138. #477 | D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774613 | 2 |
| #31774569 | 2 |
| #31774245 | 2 |
| #31774224 | 2 |
| #31774134 | 2 |
| #31774093 | 2 |
| #31774045 | 2 |
| C4×#16864641 | 2 |
| #31773962 | 2 |
| #31773892 | 2 |
| #477×C271 | 2 |
| #3305 | 271 |