Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
364 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 364 conjugacy classes of subgroups — too many to draw. Only its 129 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×#22576182 | C2 | semidirect |
| 2. #31774338 | C2 | semidirect |
| 3. #31774337 | C2 | semidirect |
| 4. #31774333 | C2 | semidirect |
| 5. #31774332 | C2 | semidirect |
| 6. #31774327 | C2 | semidirect |
| 7. C2×#22576100 | C2 | semidirect |
| 8. C2×#135×C271 | C2 | semidirect |
| 13. #22576182 | C22 | semidirect |
| 14. C2×Dic1084 | C22 | semidirect |
| 16. C2×D2168 | C22 | semidirect |
| 17. #22576106 | C22 | semidirect |
| 18. #22576104 | C22 | semidirect |
| 19. #22576103 | C22 | semidirect |
| 20. #22576101 | C22 | semidirect |
| 21. #22576100 | C22 | semidirect |
| 22. #22576100 | C22 | semidirect |
| 23. C2×C271⋊C16 | C22 | semidirect |
| 28. #135×C271 | C22 | semidirect |
| 29. C2×Q16×C271 | C22 | semidirect |
| 31. C2×D8×C271 | C22 | semidirect |
| 120. C271 | #3414 | semidirect |
| 123. C2×#135 | D271 | semidirect |
| 139. #135 | C2×D271 | semidirect |
| 141. C2×Q16 | C2×D271 | semidirect |
| 145. C2×D8 | C2×D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22576182 | 2 |
| #31774338 | 2 |
| #31774337 | 2 |
| #31774333 | 2 |
| #31774332 | 2 |
| #31774327 | 2 |
| C2×#22576100 | 2 |
| C2×#135×C271 | 2 |
| #3414 | 271 |