Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
764 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 764 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. C22×#16864655 | C2 | semidirect |
| 2. C2×#22576181 | C2 | semidirect |
| 3. #31774407 | C2 | semidirect |
| 4. #31774062 | C2 | semidirect |
| 5. #31774053 | C2 | semidirect |
| 6. #31774050 | C2 | semidirect |
| 7. #31774041 | C2 | semidirect |
| 8. #31774030 | C2 | semidirect |
| 9. #31773892 | C2 | semidirect |
| 10. C22⋊C8×D271 | C2 | semidirect |
| 11. #448×C271 | C2 | semidirect |
| 17. C2×#16864653 | C22 | semidirect |
| 23. C2×#16864644 | C22 | semidirect |
| 24. C2×#16864643 | C22 | semidirect |
| 25. C2×#16864639 | C22 | semidirect |
| 26. C2×C8×D271 | C22 | semidirect |
| 28. #22576140 | C22 | semidirect |
| 30. #22576131 | C22 | semidirect |
| 34. #22576118 | C22 | semidirect |
| 35. #22576084 | C22 | semidirect |
| 36. #22576082 | C22 | semidirect |
| 37. #22576080 | C22 | semidirect |
| 39. (C2×D271)⋊C8 | C22 | semidirect |
| 41. C2×SD16×C271 | C22 | semidirect |
| 43. #103×C271 | C22 | semidirect |
| 52. #16864655 | D4 | semidirect |
| 146. C22×C271 | #135 | semidirect |
| 175. C271 | #3002 | semidirect |
| 184. #448 | D271 | semidirect |
| 202. C2×SD16 | C2×D271 | semidirect |
| 215. #103 | C2×D271 | semidirect |
| 333. C22 | #22576181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#16864655 | 2 |
| C2×#22576181 | 2 |
| #31774407 | 2 |
| #31774062 | 2 |
| #31774053 | 2 |
| #31774050 | 2 |
| #31774041 | 2 |
| #31774030 | 2 |
| #31773892 | 2 |
| C22⋊C8×D271 | 2 |
| #448×C271 | 2 |
| #3002 | 271 |