Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
444 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 133 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 |
| 2. #31774232 | C2 | semidirect |
| 3. #31774177 | C2 | semidirect |
| 4. #31774102 | C2 | semidirect |
| 6. #31773997 | C2 | semidirect |
| 7. #31773954 | C2 | semidirect |
| 10. #22576160 | C22 | semidirect |
| 11. #22576160 | C22 | semidirect |
| 16. C4×Dic542 | C22 | semidirect |
| 18. #22576093 | C22 | semidirect |
| 19. C4⋊(C271⋊C8) | C22 | semidirect |
| 20. #22576083 | C22 | semidirect |
| 23. #22576071 | C22 | semidirect |
| 112. C271 | #3110 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774454 | 2 |
| #31774232 | 2 |
| #31774177 | 2 |
| #31774102 | 2 |
| #31774048 | 2 |
| #31773997 | 2 |
| #31773954 | 2 |
| C2×C4×D4×C271 | 2 |
| #3110 | 271 |