Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
292 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 292 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. #31773852 | C2 | semidirect |
| 4. C2×#22576070 | C2 | semidirect |
| 5. #31773661 | C2 | semidirect |
| 6. #31773658 | C2 | semidirect |
| 12. #22576087 | C4 | semidirect |
| 13. #22576084 | C4 | semidirect |
| 14. #22576081 | C4 | semidirect |
| 20. #131×C271 | C4 | semidirect |
| 98. C271 | #1765 | semidirect |
| 109. #131 | Dic271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22576087 | 2 |
| #31773893 | 2 |
| #31773852 | 2 |
| C2×#22576070 | 2 |
| #31773661 | 2 |
| #31773658 | 2 |
| C2×#131×C271 | 2 |
| #1765 | 271 |