Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
286 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 286 conjugacy classes of subgroups — too many to draw. Only its 83 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 |
|---|---|---|
| 2. #31773937 | C2 | semidirect |
| 5. #31773666 | C2 | semidirect |
| 6. #31773657 | C2 | semidirect |
| 7. #382×C271 | C2 | semidirect |
| 19. #22576088 | C4 | semidirect |
| 38. #16864638 | C2×C4 | semidirect |
| 57. C42×C271 | C2×C4 | semidirect |
| 111. C271 | #1860 | semidirect |
| 117. #382 | D271 | semidirect |
| 169. C42 | C4×D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774378 | 2 |
| #31773937 | 2 |
| C2×#22576088 | 2 |
| #31773896 | 2 |
| #31773666 | 2 |
| #31773657 | 2 |
| #382×C271 | 2 |
| #1860 | 271 |