Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
492 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 181 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 |
|---|---|---|
| 2. #31774374 | C2 | semidirect |
| 4. #31773996 | C2 | semidirect |
| 5. #31773984 | C2 | semidirect |
| 6. #31773905 | C2 | semidirect |
| 8. #31773852 | C2 | semidirect |
| 9. #427×C271 | C2 | semidirect |
| 12. C2×#16864643 | C4 | semidirect |
| 17. #22576125 | C22 | semidirect |
| 23. #22576083 | C22 | semidirect |
| 25. #22576070 | C22 | semidirect |
| 26. C8×Dic271 | C22 | semidirect |
| 30. #107×C271 | C22 | semidirect |
| 31. #106×C271 | C22 | semidirect |
| 35. C2×Dic542 | C2×C4 | semidirect |
| 43. #16864643 | C2×C4 | semidirect |
| 44. #16864643 | C2×C4 | semidirect |
| 54. C2×C8×C271 | C2×C4 | semidirect |
| 103. C271 | #2949 | semidirect |
| 110. #427 | D271 | semidirect |
| 130. #107 | C2×D271 | semidirect |
| 131. #106 | C2×D271 | semidirect |
| 152. C2×C8 | C4×D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#16864643 | 2 |
| #31774374 | 2 |
| #31774371 | 2 |
| #31773996 | 2 |
| #31773984 | 2 |
| #31773905 | 2 |
| #31773901 | 2 |
| #31773852 | 2 |
| #427×C271 | 2 |
| #2949 | 271 |