Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
394 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 394 conjugacy classes of subgroups — too many to draw. Only its 121 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. #31774509 | C2 | semidirect |
| 3. #31774239 | C2 | semidirect |
| 4. #31774198 | C2 | semidirect |
| 5. #31774103 | C2 | semidirect |
| 7. #31773999 | C2 | semidirect |
| 8. C4×#16864643 | C2 | semidirect |
| 9. #433×C271 | C2 | semidirect |
| 13. #22576160 | C22 | semidirect |
| 15. #22576152 | C22 | semidirect |
| 18. C4×Dic542 | C22 | semidirect |
| 24. #22576094 | C22 | semidirect |
| 25. #22576092 | C22 | semidirect |
| 26. #22576085 | C22 | semidirect |
| 27. #22576085 | C22 | semidirect |
| 31. C4⋊C8×C271 | C22 | semidirect |
| 33. #97×C271 | C22 | semidirect |
| 34. C4×C8×C271 | C22 | semidirect |
| 102. C271 | #3123 | semidirect |
| 112. #433 | D271 | semidirect |
| 130. C4⋊C8 | C2×D271 | semidirect |
| 136. #97 | C2×D271 | semidirect |
| 137. C4×C8 | C2×D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774509 | 2 |
| #31774371 | 2 |
| #31774239 | 2 |
| #31774198 | 2 |
| #31774103 | 2 |
| #31774050 | 2 |
| #31773999 | 2 |
| C4×#16864643 | 2 |
| #433×C271 | 2 |
| #3123 | 271 |