Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
504 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 133 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. C2×#22576180 | C2 | semidirect |
| 3. #31774461 | C2 | semidirect |
| 4. #31774378 | C2 | semidirect |
| 5. #31774122 | C2 | semidirect |
| 6. #31774115 | C2 | semidirect |
| 7. #31774096 | C2 | semidirect |
| 8. #31774091 | C2 | semidirect |
| 9. #31773925 | C2 | semidirect |
| 10. C2×#22576080 | C2 | semidirect |
| 11. #417×C271 | C2 | semidirect |
| 16. C2×#16864644 | C22 | semidirect |
| 18. C2×#16864642 | C22 | semidirect |
| 19. C2×#16864641 | C22 | semidirect |
| 21. C2×#16864639 | C22 | semidirect |
| 28. #22576125 | C22 | semidirect |
| 29. #22576122 | C22 | semidirect |
| 34. Dic271⋊C8 | C22 | semidirect |
| 35. Dic271⋊C8 | C22 | semidirect |
| 41. #103×C271 | C22 | semidirect |
| 42. #102×C271 | C22 | semidirect |
| 45. #16864654 | D4 | semidirect |
| 154. C271 | #3045 | semidirect |
| 165. #417 | D271 | semidirect |
| 194. #103 | C2×D271 | semidirect |
| 197. #102 | 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 |
| C2×#22576180 | 2 |
| #31774461 | 2 |
| #31774378 | 2 |
| #31774122 | 2 |
| #31774115 | 2 |
| #31774096 | 2 |
| #31774091 | 2 |
| #31773925 | 2 |
| C2×#22576080 | 2 |
| #417×C271 | 2 |
| #3045 | 271 |