Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
732 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 732 conjugacy classes of subgroups — too many to draw. Only its 149 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×#22576208 | C2 | semidirect |
| 2. C2×#22576188 | C2 | semidirect |
| 3. C22×#16864641 | C2 | semidirect |
| 4. #31774466 | C2 | semidirect |
| 5. #31774045 | C2 | semidirect |
| 6. #31774037 | C2 | semidirect |
| 7. #31773891 | C2 | semidirect |
| 8. #31773865 | C2 | semidirect |
| 9. #419×C271 | C2 | semidirect |
| 13. C2×#16864655 | C22 | semidirect |
| 18. C2×Q8×D271 | C22 | semidirect |
| 30. #22576083 | C22 | semidirect |
| 31. #22576080 | C22 | semidirect |
| 32. (C2×D271)⋊C8 | C22 | semidirect |
| 36. #103×C271 | C22 | semidirect |
| 45. #16864654 | D4 | semidirect |
| 74. C2×Q8×C271 | D4 | semidirect |
| 145. C271 | #3010 | semidirect |
| 153. #419 | D271 | semidirect |
| 180. #103 | C2×D271 | semidirect |
| 200. C2×Q8 | D1084 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22576208 | 2 |
| C2×#22576188 | 2 |
| C22×#16864641 | 2 |
| #31774466 | 2 |
| #31774045 | 2 |
| #31774037 | 2 |
| #31773891 | 2 |
| #31773865 | 2 |
| #419×C271 | 2 |
| #3010 | 271 |