Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
342 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 342 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 |
|---|---|---|
| 3. #31774241 | C2 | semidirect |
| 4. #31774229 | C2 | semidirect |
| 5. #31774189 | C2 | semidirect |
| 6. #31774179 | C2 | semidirect |
| 7. #31774156 | C2 | semidirect |
| 8. C4×Dic1084 | C2 | semidirect |
| 10. #31773936 | C2 | semidirect |
| 11. #498×C271 | C2 | semidirect |
| 116. C271 | #3356 | semidirect |
| 120. #498 | D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774621 | 2 |
| #31774608 | 2 |
| #31774241 | 2 |
| #31774229 | 2 |
| #31774189 | 2 |
| #31774179 | 2 |
| #31774156 | 2 |
| C4×Dic1084 | 2 |
| #31773976 | 2 |
| #31773936 | 2 |
| #498×C271 | 2 |
| #3356 | 271 |