Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
444 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 129 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. #31774454 | C2 | semidirect |
| 3. #31774233 | C2 | semidirect |
| 4. #31774178 | C2 | semidirect |
| 5. #31774103 | C2 | semidirect |
| 7. #31773999 | C2 | semidirect |
| 8. #432×C271 | C2 | semidirect |
| 12. #22576160 | C22 | semidirect |
| 13. #22576160 | C22 | semidirect |
| 18. C4×Dic542 | C22 | semidirect |
| 26. #22576094 | C22 | semidirect |
| 27. #22576085 | C22 | semidirect |
| 30. C4⋊C8×C271 | C22 | semidirect |
| 32. #97×C271 | C22 | semidirect |
| 112. C271 | #3110 | semidirect |
| 121. #432 | D271 | semidirect |
| 141. C4⋊C8 | C2×D271 | semidirect |
| 145. #97 | C2×D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774454 | 2 |
| C2×C4×D1084 | 2 |
| #31774233 | 2 |
| #31774178 | 2 |
| #31774103 | 2 |
| #31774050 | 2 |
| #31773999 | 2 |
| #432×C271 | 2 |
| #3110 | 271 |