Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
466 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 466 conjugacy classes of subgroups — too many to draw. Only its 129 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 |
|---|---|---|
| 1. #31774695 | C2 | semidirect |
| 2. C2×#22576188 | C2 | semidirect |
| 3. C2×#22576185 | C2 | semidirect |
| 4. #31774663 | C2 | semidirect |
| 5. #31774166 | C2 | semidirect |
| 6. #31774163 | C2 | semidirect |
| 7. #31773945 | C2 | semidirect |
| 8. C2×#22576076 | C2 | semidirect |
| 9. #413×C271 | C2 | semidirect |
| 12. #22576191 | C22 | semidirect |
| 16. #22576186 | C22 | semidirect |
| 22. C2×#16864641 | C22 | semidirect |
| 24. C2×#16864639 | C22 | semidirect |
| 25. #22576168 | C22 | semidirect |
| 30. #22576095 | C22 | semidirect |
| 31. #22576076 | C22 | semidirect |
| 35. #101×C271 | C22 | semidirect |
| 36. #100×C271 | C22 | semidirect |
| 147. C271 | #3068 | semidirect |
| 156. #413 | D271 | semidirect |
| 182. #101 | C2×D271 | semidirect |
| 184. #100 | C2×D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774695 | 2 |
| C2×#22576188 | 2 |
| C2×#22576185 | 2 |
| #31774663 | 2 |
| #31774166 | 2 |
| #31774163 | 2 |
| #31773945 | 2 |
| C2×#22576076 | 2 |
| #413×C271 | 2 |
| #3068 | 271 |