Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
448 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 448 conjugacy classes of subgroups — too many to draw. Only its 127 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. #31774452 | C2 | semidirect |
| 3. #31774229 | C2 | semidirect |
| 4. #31774184 | C2 | semidirect |
| 5. #31774103 | C2 | semidirect |
| 6. #31774102 | C2 | semidirect |
| 8. #31773988 | C2 | semidirect |
| 9. #31773984 | C2 | semidirect |
| 10. #31773949 | C2 | semidirect |
| 11. #476×C271 | C2 | semidirect |
| 16. #22576160 | C22 | semidirect |
| 21. #22576125 | C22 | semidirect |
| 31. #22576091 | C22 | semidirect |
| 32. C4⋊(C271⋊C8) | C22 | semidirect |
| 33. #22576085 | C22 | semidirect |
| 34. #22576083 | C22 | semidirect |
| 37. C8×Dic271 | C22 | semidirect |
| 38. C4⋊Q8×C271 | C22 | semidirect |
| 40. #106×C271 | C22 | semidirect |
| 41. C4⋊C8×C271 | C22 | semidirect |
| 105. C4×D271 | SD16 | semidirect |
| 146. C271 | #3101 | semidirect |
| 152. #476 | D271 | semidirect |
| 164. C4⋊Q8 | C2×D271 | semidirect |
| 181. #106 | C2×D271 | semidirect |
| 183. C4⋊C8 | C2×D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774452 | 2 |
| C4×D4×D271 | 2 |
| #31774229 | 2 |
| #31774184 | 2 |
| #31774103 | 2 |
| #31774102 | 2 |
| #31774049 | 2 |
| #31773988 | 2 |
| #31773984 | 2 |
| #31773949 | 2 |
| #476×C271 | 2 |
| #3101 | 271 |