Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
286 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 286 conjugacy classes of subgroups — too many to draw. Only its 89 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 |
| 4. #31773762 | C2 | semidirect |
| 5. #31773665 | C2 | semidirect |
| 6. #31773658 | C2 | semidirect |
| 19. #22576087 | C4 | semidirect |
| 30. #16864638 | C2×C4 | semidirect |
| 42. C4×Dic271 | C2×C4 | semidirect |
| 111. C271 | #1860 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774380 | 2 |
| #31773937 | 2 |
| C2×#22576087 | 2 |
| #31773762 | 2 |
| #31773665 | 2 |
| #31773658 | 2 |
| #417×C271 | 2 |
| #1860 | 271 |