Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
504 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 504 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. C2×#22576186 | C2 | semidirect |
| 2. C2×#22576180 | C2 | semidirect |
| 3. #31774377 | C2 | semidirect |
| 4. #31774116 | C2 | semidirect |
| 5. #31774109 | C2 | semidirect |
| 6. #31774094 | C2 | semidirect |
| 7. #31774089 | C2 | semidirect |
| 8. #31773924 | C2 | semidirect |
| 9. #31773898 | C2 | semidirect |
| 10. C2×#22576081 | C2 | semidirect |
| 11. #535×C271 | C2 | semidirect |
| 15. C2×#16864644 | C22 | semidirect |
| 17. C2×#16864642 | C22 | semidirect |
| 18. C2×#16864641 | C22 | semidirect |
| 20. C2×#16864639 | C22 | semidirect |
| 23. C4×Dic542 | C22 | semidirect |
| 24. C4×D1084 | C22 | semidirect |
| 29. C4⋊(C271⋊C8) | C22 | semidirect |
| 30. C4⋊(C271⋊C8) | C22 | semidirect |
| 31. #22576084 | C22 | semidirect |
| 34. #22576081 | C22 | semidirect |
| 44. #16864654 | D4 | semidirect |
| 154. C271 | #3045 | semidirect |
| 158. #535 | D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22576186 | 2 |
| C2×#22576180 | 2 |
| #31774377 | 2 |
| #31774116 | 2 |
| #31774109 | 2 |
| #31774094 | 2 |
| #31774089 | 2 |
| #31773924 | 2 |
| #31773898 | 2 |
| C2×#22576081 | 2 |
| #535×C271 | 2 |
| #3045 | 271 |