Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
548 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 548 conjugacy classes of subgroups — too many to draw. Only its 135 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. C2×#22576188 | C2 | semidirect |
| 2. C2×#22576185 | C2 | semidirect |
| 3. #31774443 | C2 | semidirect |
| 4. C2×#22576122 | C2 | semidirect |
| 5. #31774115 | C2 | semidirect |
| 6. #31774111 | C2 | semidirect |
| 7. #31774101 | C2 | semidirect |
| 8. #31774091 | C2 | semidirect |
| 9. #31773920 | C2 | semidirect |
| 10. #31773896 | C2 | semidirect |
| 11. #417×C271 | C2 | semidirect |
| 22. #22576158 | C22 | semidirect |
| 23. #22576156 | C22 | semidirect |
| 24. #22576149 | C22 | semidirect |
| 25. #22576147 | C22 | semidirect |
| 36. Dic271⋊C8 | C22 | semidirect |
| 37. Dic271⋊C8 | C22 | semidirect |
| 38. #22576083 | C22 | semidirect |
| 39. #22576080 | C22 | semidirect |
| 43. #103×C271 | C22 | semidirect |
| 44. #102×C271 | C22 | semidirect |
| 51. C2×D1084 | D4 | semidirect |
| 158. Dic271 | AGL(1,ℤ/8) | semidirect |
| 166. C271 | #3036 | semidirect |
| 178. #417 | D271 | semidirect |
| 209. #103 | C2×D271 | semidirect |
| 211. #102 | C2×D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22576188 | 2 |
| C2×#22576185 | 2 |
| #31774443 | 2 |
| C2×#22576122 | 2 |
| #31774115 | 2 |
| #31774111 | 2 |
| #31774101 | 2 |
| #31774091 | 2 |
| #31773920 | 2 |
| #31773896 | 2 |
| #417×C271 | 2 |
| #3036 | 271 |