Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
370 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 370 conjugacy classes of subgroups — too many to draw. Only its 113 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. #31774699 | C2 | semidirect |
| 2. #31774334 | C2 | semidirect |
| 3. #31774332 | C2 | semidirect |
| 4. #31774330 | C2 | semidirect |
| 5. C2×D4336 | C2 | semidirect |
| 6. D16×D271 | C2 | semidirect |
| 7. #31774313 | C2 | semidirect |
| 8. #508×C271 | C2 | semidirect |
| 12. #22576183 | C22 | semidirect |
| 13. C2×D2168 | C22 | semidirect |
| 14. D8×D271 | C22 | semidirect |
| 16. #22576103 | C22 | semidirect |
| 17. D4336 | C22 | semidirect |
| 18. D4336 | C22 | semidirect |
| 19. #22576101 | C22 | semidirect |
| 20. #22576100 | C22 | semidirect |
| 21. #22576099 | C22 | semidirect |
| 22. C16×D271 | C22 | semidirect |
| 23. #135×C271 | C22 | semidirect |
| 24. Q32×C271 | C22 | semidirect |
| 25. SD32×C271 | C22 | semidirect |
| 26. D16×C271 | C22 | semidirect |
| 27. C2×C16×C271 | C22 | semidirect |
| 84. C271 | #3415 | semidirect |
| 90. #508 | D271 | semidirect |
| 98. #135 | C2×D271 | semidirect |
| 102. Q32 | C2×D271 | semidirect |
| 104. SD32 | C2×D271 | semidirect |
| 108. D16 | C2×D271 | semidirect |
| 112. C2×C16 | C2×D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774699 | 2 |
| #31774334 | 2 |
| #31774332 | 2 |
| #31774330 | 2 |
| C2×D4336 | 2 |
| D16×D271 | 2 |
| #31774313 | 2 |
| #508×C271 | 2 |
| #3415 | 271 |