Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
526 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 526 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×#22576185 | C2 | semidirect |
| 2. C22×D2168 | C2 | semidirect |
| 3. #31774461 | C2 | semidirect |
| 4. #31774371 | C2 | semidirect |
| 5. #31774115 | C2 | semidirect |
| 6. #31774091 | C2 | semidirect |
| 7. #31773923 | C2 | semidirect |
| 8. #31773901 | C2 | semidirect |
| 9. #416×C271 | C2 | semidirect |
| 13. C2×#16864641 | C22 | semidirect |
| 16. C2×#16864639 | C22 | semidirect |
| 18. #22576156 | C22 | semidirect |
| 19. #22576149 | C22 | semidirect |
| 23. #22576122 | C22 | semidirect |
| 26. Dic271⋊C8 | C22 | semidirect |
| 27. #22576080 | C22 | semidirect |
| 31. #103×C271 | C22 | semidirect |
| 32. #102×C271 | C22 | semidirect |
| 40. C2×D1084 | D4 | semidirect |
| 121. C271 | #3041 | semidirect |
| 131. #416 | D271 | semidirect |
| 152. #103 | C2×D271 | semidirect |
| 154. #102 | C2×D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22576185 | 2 |
| C22×D2168 | 2 |
| #31774461 | 2 |
| #31774371 | 2 |
| #31774115 | 2 |
| #31774091 | 2 |
| #31773923 | 2 |
| #31773901 | 2 |
| #416×C271 | 2 |
| #3041 | 271 |