Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
386 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 117 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. C2×#22576125 | C2 | semidirect |
| 4. #31774203 | C2 | semidirect |
| 5. #31774122 | C2 | semidirect |
| 6. #31774052 | C2 | semidirect |
| 8. #31774001 | C2 | semidirect |
| 9. #31773996 | C2 | semidirect |
| 10. #31773951 | C2 | semidirect |
| 11. #484×C271 | C2 | semidirect |
| 131. C271 | #3117 | semidirect |
| 135. #484 | D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774433 | 2 |
| C2×#22576125 | 2 |
| #31774215 | 2 |
| #31774203 | 2 |
| #31774122 | 2 |
| #31774052 | 2 |
| #31774038 | 2 |
| #31774001 | 2 |
| #31773996 | 2 |
| #31773951 | 2 |
| #484×C271 | 2 |
| #3117 | 271 |