Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
420 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 137 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. #31774238 | C2 | semidirect |
| 3. #31774232 | C2 | semidirect |
| 4. #31774227 | C2 | semidirect |
| 5. #31774221 | C2 | semidirect |
| 6. #31774215 | C2 | semidirect |
| 7. #31774210 | C2 | semidirect |
| 8. #31773933 | C2 | semidirect |
| 9. #31773891 | C2 | semidirect |
| 10. C2×C22⋊(C271⋊C8) | C2 | semidirect |
| 11. C2×#117×C271 | C2 | semidirect |
| 23. #22576093 | C22 | semidirect |
| 24. #22576093 | C22 | semidirect |
| 25. #22576091 | C22 | semidirect |
| 26. #22576091 | C22 | semidirect |
| 27. #22576083 | C22 | semidirect |
| 28. #22576083 | C22 | semidirect |
| 29. #22576080 | C22 | semidirect |
| 30. #22576080 | C22 | semidirect |
| 143. C271 | #3091 | semidirect |
| 146. C2×#117 | D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774408 | 2 |
| #31774238 | 2 |
| #31774232 | 2 |
| #31774227 | 2 |
| #31774221 | 2 |
| #31774215 | 2 |
| #31774210 | 2 |
| #31773933 | 2 |
| #31773891 | 2 |
| C2×C22⋊(C271⋊C8) | 2 |
| C2×#117×C271 | 2 |
| #3091 | 271 |