Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
484 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 484 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 |
|---|---|---|
| 1. #31774452 | C2 | semidirect |
| 3. #31774260 | C2 | semidirect |
| 4. #31774245 | C2 | semidirect |
| 5. #31774244 | C2 | semidirect |
| 6. #31774243 | C2 | semidirect |
| 7. #31773900 | C2 | semidirect |
| 8. C4×#16864637 | C2 | semidirect |
| 9. #486×C271 | C2 | semidirect |
| 14. #22576160 | C22 | semidirect |
| 19. #22576151 | C22 | semidirect |
| 26. #22576082 | C22 | semidirect |
| 27. #22576081 | C22 | semidirect |
| 28. #22576080 | C22 | semidirect |
| 29. #22576070 | C22 | semidirect |
| 30. C4×C271⋊C8 | C22 | semidirect |
| 31. C4⋊Q8×C271 | C22 | semidirect |
| 33. #102×C271 | C22 | semidirect |
| 34. C4×C8×C271 | C22 | semidirect |
| 123. C271 | #3138 | semidirect |
| 131. #486 | D271 | semidirect |
| 139. C4⋊Q8 | C2×D271 | semidirect |
| 155. #102 | C2×D271 | semidirect |
| 158. 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 |
| #127×D271 | 2 |
| #31774260 | 2 |
| #31774245 | 2 |
| #31774244 | 2 |
| #31774243 | 2 |
| #31773900 | 2 |
| C4×#16864637 | 2 |
| #486×C271 | 2 |
| #3138 | 271 |