Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
490 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 490 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×#22576190 | C2 | semidirect |
| 2. C22×#16864643 | C2 | semidirect |
| 4. #31774374 | C2 | semidirect |
| 5. #31774122 | C2 | semidirect |
| 6. #31774096 | C2 | semidirect |
| 7. #31773923 | C2 | semidirect |
| 8. #31773901 | C2 | semidirect |
| 9. #416×C271 | C2 | semidirect |
| 13. C2×#16864644 | C22 | semidirect |
| 16. C2×#16864642 | C22 | semidirect |
| 23. #22576125 | C22 | semidirect |
| 26. Dic271⋊C8 | C22 | semidirect |
| 31. #103×C271 | C22 | semidirect |
| 32. #102×C271 | C22 | semidirect |
| 36. C2×Dic542 | D4 | semidirect |
| 116. C271 | #3043 | semidirect |
| 126. #416 | D271 | semidirect |
| 147. #103 | C2×D271 | semidirect |
| 149. #102 | C2×D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22576190 | 2 |
| C22×#16864643 | 2 |
| #31774461 | 2 |
| #31774374 | 2 |
| #31774122 | 2 |
| #31774096 | 2 |
| #31773923 | 2 |
| #31773901 | 2 |
| #416×C271 | 2 |
| #3043 | 271 |