Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
404 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 133 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. #31774263 | C2 | semidirect |
| 3. #31774259 | C2 | semidirect |
| 4. #31774254 | C2 | semidirect |
| 5. #31774245 | C2 | semidirect |
| 6. #31773901 | C2 | semidirect |
| 7. #31773896 | C2 | semidirect |
| 8. #31773891 | C2 | semidirect |
| 9. C2×#22576080 | C2 | semidirect |
| 10. #31773853 | C2 | semidirect |
| 11. #544×C271 | C2 | semidirect |
| 21. #22576083 | C22 | semidirect |
| 22. #22576083 | C22 | semidirect |
| 23. #22576083 | C22 | semidirect |
| 28. #22576080 | C22 | semidirect |
| 29. #22576080 | C22 | semidirect |
| 30. #22576080 | C22 | semidirect |
| 31. #22576071 | C22 | semidirect |
| 32. C4×C271⋊C8 | C22 | semidirect |
| 34. C4⋊Q8×C271 | C22 | semidirect |
| 36. #125×C271 | C22 | semidirect |
| 135. C271 | #3136 | semidirect |
| 137. #544 | D271 | semidirect |
| 153. C4⋊Q8 | C2×D271 | semidirect |
| 156. #125 | C2×D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774466 | 2 |
| #31774263 | 2 |
| #31774259 | 2 |
| #31774254 | 2 |
| #31774245 | 2 |
| #31773901 | 2 |
| #31773896 | 2 |
| #31773891 | 2 |
| C2×#22576080 | 2 |
| #31773853 | 2 |
| #544×C271 | 2 |
| #3136 | 271 |