Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
500 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 500 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×#22576180 | C2 | semidirect |
| 2. C22×#16864637 | C2 | semidirect |
| 3. #31774409 | C2 | semidirect |
| 4. #31774404 | C2 | semidirect |
| 5. #31774154 | C2 | semidirect |
| 6. #31774149 | C2 | semidirect |
| 7. #31774146 | C2 | semidirect |
| 8. #31774142 | C2 | semidirect |
| 9. #31773933 | C2 | semidirect |
| 10. #31773894 | C2 | semidirect |
| 11. #416×C271 | C2 | semidirect |
| 15. C2×#16864644 | C22 | semidirect |
| 16. C2×#16864642 | C22 | semidirect |
| 17. C2×#16864641 | C22 | semidirect |
| 18. C2×#16864639 | C22 | semidirect |
| 34. #22576093 | C22 | semidirect |
| 35. #22576091 | C22 | semidirect |
| 36. #22576085 | C22 | semidirect |
| 37. #22576082 | C22 | semidirect |
| 41. #103×C271 | C22 | semidirect |
| 42. #102×C271 | C22 | semidirect |
| 63. C2×C271⋊C8 | D4 | semidirect |
| 148. C271 | #3054 | semidirect |
| 160. #416 | D271 | semidirect |
| 189. #103 | C2×D271 | semidirect |
| 191. #102 | C2×D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22576180 | 2 |
| C22×#16864637 | 2 |
| #31774409 | 2 |
| #31774404 | 2 |
| #31774154 | 2 |
| #31774149 | 2 |
| #31774146 | 2 |
| #31774142 | 2 |
| #31773933 | 2 |
| #31773894 | 2 |
| #416×C271 | 2 |
| #3054 | 271 |