Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
414 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 414 conjugacy classes of subgroups — too many to draw. Only its 125 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. C2×#22576118 | C2 | semidirect |
| 3. #31774241 | C2 | semidirect |
| 4. #31774240 | C2 | semidirect |
| 5. #31774224 | C2 | semidirect |
| 6. #31774223 | C2 | semidirect |
| 7. #31773940 | C2 | semidirect |
| 8. #31773899 | C2 | semidirect |
| 9. #31773896 | C2 | semidirect |
| 10. #31773860 | C2 | semidirect |
| 11. #428×C271 | C2 | semidirect |
| 30. #22576093 | C22 | semidirect |
| 31. #22576091 | C22 | semidirect |
| 32. #22576085 | C22 | semidirect |
| 33. #22576083 | C22 | semidirect |
| 34. #22576082 | C22 | semidirect |
| 35. #22576080 | C22 | semidirect |
| 41. #107×C271 | C22 | semidirect |
| 42. #106×C271 | C22 | semidirect |
| 152. C271 | #3093 | semidirect |
| 161. #428 | D271 | semidirect |
| 187. #107 | C2×D271 | semidirect |
| 189. #106 | C2×D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774409 | 2 |
| C2×#22576118 | 2 |
| #31774241 | 2 |
| #31774240 | 2 |
| #31774224 | 2 |
| #31774223 | 2 |
| #31773940 | 2 |
| #31773899 | 2 |
| #31773896 | 2 |
| #31773860 | 2 |
| #428×C271 | 2 |
| #3093 | 271 |