Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
548 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 548 conjugacy classes of subgroups — too many to draw. Only its 131 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×#22576187 | C2 | semidirect |
| 2. #31774448 | C2 | semidirect |
| 3. C4×D4×D271 | C2 | semidirect |
| 4. #31774115 | C2 | semidirect |
| 5. #31774114 | C2 | semidirect |
| 6. #31774099 | C2 | semidirect |
| 7. #31774093 | C2 | semidirect |
| 8. #31774092 | C2 | semidirect |
| 9. #31773919 | C2 | semidirect |
| 10. #31773897 | C2 | semidirect |
| 11. #461×C271 | C2 | semidirect |
| 20. #22576157 | C22 | semidirect |
| 21. #22576149 | C22 | semidirect |
| 34. C4⋊(C271⋊C8) | C22 | semidirect |
| 35. Dic271⋊C8 | C22 | semidirect |
| 36. #22576084 | C22 | semidirect |
| 37. #22576082 | C22 | semidirect |
| 38. #22576080 | C22 | semidirect |
| 40. C4⋊Q8×C271 | C22 | semidirect |
| 42. C4⋊C8×C271 | C22 | semidirect |
| 43. #103×C271 | C22 | semidirect |
| 54. D4×D271 | D4 | semidirect |
| 146. C4×C271 | AGL(1,ℤ/8) | semidirect |
| 160. C271 | #3036 | semidirect |
| 168. #461 | D271 | semidirect |
| 182. C4⋊Q8 | C2×D271 | semidirect |
| 200. C4⋊C8 | C2×D271 | semidirect |
| 202. #103 | C2×D271 | semidirect |
| 311. C4 | #22576187 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22576187 | 2 |
| #31774448 | 2 |
| C4×D4×D271 | 2 |
| #31774115 | 2 |
| #31774114 | 2 |
| #31774099 | 2 |
| #31774093 | 2 |
| #31774092 | 2 |
| #31773919 | 2 |
| #31773897 | 2 |
| #461×C271 | 2 |
| #3036 | 271 |