Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
492 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 189 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. #31773999 | C2 | semidirect |
| 5. C4×#16864643 | C2 | semidirect |
| 6. #31773935 | C2 | semidirect |
| 7. #31773907 | C2 | semidirect |
| 9. #405×C271 | C2 | semidirect |
| 12. C2×#16864643 | C4 | semidirect |
| 15. C4×Dic542 | C22 | semidirect |
| 23. #22576094 | C22 | semidirect |
| 24. #22576092 | C22 | semidirect |
| 25. #22576085 | C22 | semidirect |
| 30. #97×C271 | C22 | semidirect |
| 31. C4×C8×C271 | C22 | semidirect |
| 35. C2×Dic542 | C2×C4 | semidirect |
| 43. #16864643 | C2×C4 | semidirect |
| 44. #16864643 | C2×C4 | semidirect |
| 56. C2×C8×C271 | C2×C4 | semidirect |
| 103. C271 | #2949 | semidirect |
| 113. #405 | D271 | semidirect |
| 134. #97 | C2×D271 | semidirect |
| 135. C4×C8 | C2×D271 | semidirect |
| 151. 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 |
| #31773999 | 2 |
| C4×#16864643 | 2 |
| #31773935 | 2 |
| #31773907 | 2 |
| #31773903 | 2 |
| #405×C271 | 2 |
| #2949 | 271 |