Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
374 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 374 conjugacy classes of subgroups — too many to draw. Only its 123 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. #31774300 | C2 | semidirect |
| 3. #31774230 | C2 | semidirect |
| 4. #31774221 | C2 | semidirect |
| 5. #31774182 | C2 | semidirect |
| 6. #31774174 | C2 | semidirect |
| 7. #31774145 | C2 | semidirect |
| 8. C4×#16864641 | C2 | semidirect |
| 9. #31773975 | C2 | semidirect |
| 10. #31773940 | C2 | semidirect |
| 11. #556×C271 | C2 | semidirect |
| 85. C271⋊C8 | #41 | semidirect |
| 122. C271 | #3353 | semidirect |
| 124. #556 | D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774551 | 2 |
| #31774300 | 2 |
| #31774230 | 2 |
| #31774221 | 2 |
| #31774182 | 2 |
| #31774174 | 2 |
| #31774145 | 2 |
| C4×#16864641 | 2 |
| #31773975 | 2 |
| #31773940 | 2 |
| #556×C271 | 2 |
| #3353 | 271 |