Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
398 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 125 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. #31774612 | C2 | semidirect |
| 2. #31774247 | C2 | semidirect |
| 3. #31774235 | C2 | semidirect |
| 4. #31774187 | C2 | semidirect |
| 5. #31774128 | C2 | semidirect |
| 6. #31774099 | C2 | semidirect |
| 7. #31774042 | C2 | semidirect |
| 8. C4×#16864639 | C2 | semidirect |
| 9. D4×C271⋊C8 | C2 | semidirect |
| 10. #31773893 | C2 | semidirect |
| 11. #547×C271 | C2 | semidirect |
| 130. C271 | #3303 | semidirect |
| 133. #547 | D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774612 | 2 |
| #31774247 | 2 |
| #31774235 | 2 |
| #31774187 | 2 |
| #31774128 | 2 |
| #31774099 | 2 |
| #31774042 | 2 |
| C4×#16864639 | 2 |
| D4×C271⋊C8 | 2 |
| #31773893 | 2 |
| #547×C271 | 2 |
| #3303 | 271 |