Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
392 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 392 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 |
|---|---|---|
| 2. #125×D271 | C2 | semidirect |
| 3. #31774264 | C2 | semidirect |
| 4. #31774260 | C2 | semidirect |
| 5. #31774254 | C2 | semidirect |
| 6. #31774252 | C2 | semidirect |
| 7. #31774251 | C2 | semidirect |
| 8. #31773897 | C2 | semidirect |
| 9. #31773895 | C2 | semidirect |
| 10. C4×#16864637 | C2 | semidirect |
| 11. #488×C271 | C2 | semidirect |
| 114. C271 | #3142 | semidirect |
| 123. #488 | D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774446 | 2 |
| #125×D271 | 2 |
| #31774264 | 2 |
| #31774260 | 2 |
| #31774254 | 2 |
| #31774252 | 2 |
| #31774251 | 2 |
| #31773897 | 2 |
| #31773895 | 2 |
| C4×#16864637 | 2 |
| #488×C271 | 2 |
| #3142 | 271 |