Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
520 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 520 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×#22576188 | C2 | semidirect |
| 2. #31774543 | C2 | semidirect |
| 3. #31774281 | C2 | semidirect |
| 4. #31774143 | C2 | semidirect |
| 5. #31774113 | C2 | semidirect |
| 6. #31774061 | C2 | semidirect |
| 7. #31774033 | C2 | semidirect |
| 8. C4×D2168 | C2 | semidirect |
| 9. #436×C271 | C2 | semidirect |
| 11. C22×D1084 | C22 | semidirect |
| 13. C2×Dic1084 | C22 | semidirect |
| 14. C2×#16864643 | C22 | semidirect |
| 15. C2×#16864643 | C22 | semidirect |
| 19. #22576148 | C22 | semidirect |
| 21. #22576139 | C22 | semidirect |
| 25. C4×D1084 | C22 | semidirect |
| 27. #22576094 | C22 | semidirect |
| 28. #22576085 | C22 | semidirect |
| 29. #22576082 | C22 | semidirect |
| 30. #22576082 | C22 | semidirect |
| 31. C2×M16×C271 | C22 | semidirect |
| 33. C4⋊C8×C271 | C22 | semidirect |
| 34. C22⋊C8×C271 | C22 | semidirect |
| 35. C4×C8×C271 | C22 | semidirect |
| 54. D2168 | D4 | semidirect |
| 124. C271 | #3273 | semidirect |
| 134. #436 | D271 | semidirect |
| 144. C2×M16 | C2×D271 | semidirect |
| 155. C4⋊C8 | C2×D271 | semidirect |
| 159. C22⋊C8 | C2×D271 | semidirect |
| 160. C4×C8 | C2×D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22576188 | 2 |
| #31774543 | 2 |
| #31774281 | 2 |
| #31774143 | 2 |
| #31774113 | 2 |
| #31774061 | 2 |
| #31774033 | 2 |
| C4×D2168 | 2 |
| #436×C271 | 2 |
| #3273 | 271 |