Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
462 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 462 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. #31774604 | C2 | semidirect |
| 2. #31774243 | C2 | semidirect |
| 3. #31774213 | C2 | semidirect |
| 4. #31774187 | C2 | semidirect |
| 5. #31774124 | C2 | semidirect |
| 6. #31774094 | C2 | semidirect |
| 7. #31774048 | C2 | semidirect |
| 8. C4×#16864642 | C2 | semidirect |
| 9. D4×C271⋊C8 | C2 | semidirect |
| 10. C2×#22576081 | C2 | semidirect |
| 13. C2×#16864642 | C22 | semidirect |
| 14. C22×C271⋊C8 | C22 | semidirect |
| 15. #22576160 | C22 | semidirect |
| 17. #22576139 | C22 | semidirect |
| 19. C4×Dic542 | C22 | semidirect |
| 21. C2×C4⋊Dic271 | C22 | semidirect |
| 22. #22576091 | C22 | semidirect |
| 23. #22576091 | C22 | semidirect |
| 24. C4⋊(C271⋊C8) | C22 | semidirect |
| 25. #22576083 | C22 | semidirect |
| 28. #22576081 | C22 | semidirect |
| 29. #22576081 | C22 | semidirect |
| 30. #22576081 | C22 | semidirect |
| 31. C22⋊(C271⋊C8) | C22 | semidirect |
| 32. C4×C271⋊C8 | C22 | semidirect |
| 100. D4×C271 | SD16 | semidirect |
| 136. C271 | #3295 | semidirect |
| 230. D4 | #16864642 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774604 | 2 |
| #31774243 | 2 |
| #31774213 | 2 |
| #31774187 | 2 |
| #31774124 | 2 |
| #31774094 | 2 |
| #31774048 | 2 |
| C4×#16864642 | 2 |
| D4×C271⋊C8 | 2 |
| C2×#22576081 | 2 |
| D42×C271 | 2 |
| #3295 | 271 |