Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
386 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 125 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 |
|---|---|---|
| 3. #31774241 | C2 | semidirect |
| 4. #31774240 | C2 | semidirect |
| 5. #31774234 | C2 | semidirect |
| 6. #31774229 | C2 | semidirect |
| 7. #31773933 | C2 | semidirect |
| 8. #31773907 | C2 | semidirect |
| 9. C2×#22576083 | C2 | semidirect |
| 11. #428×C271 | C2 | semidirect |
| 126. C271 | #3097 | semidirect |
| 134. #428 | D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774473 | 2 |
| #31774378 | 2 |
| #31774241 | 2 |
| #31774240 | 2 |
| #31774234 | 2 |
| #31774229 | 2 |
| #31773933 | 2 |
| #31773907 | 2 |
| C2×#22576083 | 2 |
| #31773865 | 2 |
| #428×C271 | 2 |
| #3097 | 271 |