Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
454 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 454 conjugacy classes of subgroups — too many to draw. Only its 125 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. #31774711 | C2 | semidirect |
| 2. #31774709 | C2 | semidirect |
| 3. #31774699 | C2 | semidirect |
| 4. #31774281 | C2 | semidirect |
| 5. #31774173 | C2 | semidirect |
| 6. #31774168 | C2 | semidirect |
| 7. #31774160 | C2 | semidirect |
| 8. #31774076 | C2 | semidirect |
| 9. #31774071 | C2 | semidirect |
| 10. #31774015 | C2 | semidirect |
| 11. #443×C271 | C2 | semidirect |
| 12. #22576207 | C22 | semidirect |
| 16. #22576190 | C22 | semidirect |
| 19. #22576188 | C22 | semidirect |
| 26. C2×Dic1084 | C22 | semidirect |
| 29. C2×#16864643 | C22 | semidirect |
| 33. #22576166 | C22 | semidirect |
| 34. #22576148 | C22 | semidirect |
| 35. #22576096 | C22 | semidirect |
| 37. #22576088 | C22 | semidirect |
| 38. #22576078 | C22 | semidirect |
| 39. #22576076 | C22 | semidirect |
| 41. #131×C271 | C22 | semidirect |
| 42. #108×C271 | C22 | semidirect |
| 43. #104×C271 | C22 | semidirect |
| 44. C4×C8×C271 | C22 | semidirect |
| 149. C271 | #3290 | semidirect |
| 161. #443 | D271 | semidirect |
| 185. #131 | C2×D271 | semidirect |
| 188. #108 | C2×D271 | semidirect |
| 191. #104 | C2×D271 | semidirect |
| 194. C4×C8 | C2×D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774711 | 2 |
| #31774709 | 2 |
| #31774699 | 2 |
| #31774281 | 2 |
| #31774173 | 2 |
| #31774168 | 2 |
| #31774160 | 2 |
| #31774076 | 2 |
| #31774071 | 2 |
| #31774015 | 2 |
| #443×C271 | 2 |
| #3290 | 271 |