Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
292 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 105 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 |
|---|---|---|
| 4. #31773853 | C2 | semidirect |
| 5. C2×#22576071 | C2 | semidirect |
| 6. #31773661 | C2 | semidirect |
| 7. #339×C271 | C2 | semidirect |
| 10. #22576168 | C4 | semidirect |
| 16. #22576088 | C4 | semidirect |
| 17. #22576083 | C4 | semidirect |
| 18. #22576080 | C4 | semidirect |
| 98. C271 | #1765 | semidirect |
| 106. #339 | D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22576168 | 2 |
| C2×#22576088 | 2 |
| #31773891 | 2 |
| #31773853 | 2 |
| C2×#22576071 | 2 |
| #31773661 | 2 |
| #339×C271 | 2 |
| #1765 | 271 |