Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
524 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 524 conjugacy classes of subgroups — too many to draw. Only its 141 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. C22×#16864639 | C2 | semidirect |
| 2. C2×#22576167 | C2 | semidirect |
| 3. #31774461 | C2 | semidirect |
| 4. #31774148 | C2 | semidirect |
| 5. #31774131 | C2 | semidirect |
| 6. #31773933 | C2 | semidirect |
| 7. #31773902 | C2 | semidirect |
| 8. #31773901 | C2 | semidirect |
| 9. #535×C271 | C2 | semidirect |
| 16. C2×#16864638 | C22 | semidirect |
| 18. C22×C271⋊C8 | C22 | semidirect |
| 21. #22576134 | C22 | semidirect |
| 24. #22576093 | C22 | semidirect |
| 25. #22576091 | C22 | semidirect |
| 26. #22576081 | C22 | semidirect |
| 27. #22576080 | C22 | semidirect |
| 32. #121×C271 | C22 | semidirect |
| 46. C2×C271⋊C8 | D4 | semidirect |
| 125. C271 | #3058 | semidirect |
| 130. #535 | D271 | semidirect |
| 152. #121 | C2×D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#16864639 | 2 |
| C2×#22576167 | 2 |
| #31774461 | 2 |
| #31774148 | 2 |
| #31774131 | 2 |
| #31773933 | 2 |
| #31773902 | 2 |
| #31773901 | 2 |
| #535×C271 | 2 |
| #3058 | 271 |