Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
504 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 141 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×#22576168 | C2 | semidirect |
| 2. #31774475 | C2 | semidirect |
| 3. #31774464 | C2 | semidirect |
| 4. #31774147 | C2 | semidirect |
| 5. #31774140 | C2 | semidirect |
| 6. #31774130 | C2 | semidirect |
| 7. #31774123 | C2 | semidirect |
| 8. #31773939 | C2 | semidirect |
| 9. #31773893 | C2 | semidirect |
| 10. C2×#22576081 | C2 | semidirect |
| 11. C2×AGL(1,ℤ/8)×C271 | C2 | semidirect |
| 14. C2×#16864637 | C22 | semidirect |
| 16. C2×C8×D271 | C22 | semidirect |
| 20. #22576136 | C22 | semidirect |
| 25. #22576131 | C22 | semidirect |
| 29. #22576094 | C22 | semidirect |
| 30. #22576092 | C22 | semidirect |
| 31. #22576084 | C22 | semidirect |
| 32. #22576084 | C22 | semidirect |
| 35. #22576081 | C22 | semidirect |
| 36. #22576081 | C22 | semidirect |
| 83. M16×C271 | D4 | semidirect |
| 151. C271 | #3062 | semidirect |
| 153. C2×AGL(1,ℤ/8) | D271 | semidirect |
| 220. M16 | C22⋊D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22576168 | 2 |
| #31774475 | 2 |
| #31774464 | 2 |
| #31774147 | 2 |
| #31774140 | 2 |
| #31774130 | 2 |
| #31774123 | 2 |
| #31773939 | 2 |
| #31773893 | 2 |
| C2×#22576081 | 2 |
| C2×AGL(1,ℤ/8)×C271 | 2 |
| #3062 | 271 |