Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
494 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 494 conjugacy classes of subgroups — too many to draw. Only its 141 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. #31774551 | C2 | semidirect |
| 2. #31774243 | C2 | semidirect |
| 3. #31774208 | C2 | semidirect |
| 4. #31774177 | C2 | semidirect |
| 5. #31774131 | C2 | semidirect |
| 6. #31774089 | C2 | semidirect |
| 7. #31774031 | C2 | semidirect |
| 8. C4×#16864639 | C2 | semidirect |
| 9. D4×C271⋊C8 | C2 | semidirect |
| 10. C2×#22576081 | C2 | semidirect |
| 11. D42×C271 | C2 | semidirect |
| 14. C2×#16864639 | C22 | semidirect |
| 15. C22×C271⋊C8 | C22 | semidirect |
| 16. #22576160 | C22 | semidirect |
| 19. #22576134 | C22 | semidirect |
| 20. C4×D1084 | C22 | semidirect |
| 21. C2×C4⋊Dic271 | C22 | semidirect |
| 22. #22576093 | C22 | semidirect |
| 23. #22576093 | C22 | semidirect |
| 24. C4⋊(C271⋊C8) | C22 | semidirect |
| 27. #22576081 | C22 | semidirect |
| 28. #22576081 | C22 | semidirect |
| 29. #22576081 | C22 | semidirect |
| 30. #22576080 | C22 | semidirect |
| 31. C22⋊(C271⋊C8) | C22 | semidirect |
| 32. C4×C271⋊C8 | C22 | semidirect |
| 103. D4×C271 | D8 | semidirect |
| 104. D4×C271 | #41 | semidirect |
| 142. C271 | #3294 | semidirect |
| 145. D42 | D271 | semidirect |
| 239. D4 | #16864639 | semidirect |
| 240. D4 | #16864653 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774551 | 2 |
| #31774243 | 2 |
| #31774208 | 2 |
| #31774177 | 2 |
| #31774131 | 2 |
| #31774089 | 2 |
| #31774031 | 2 |
| C4×#16864639 | 2 |
| D4×C271⋊C8 | 2 |
| C2×#22576081 | 2 |
| D42×C271 | 2 |
| #3294 | 271 |