Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
454 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 454 conjugacy classes of subgroups — too many to draw. Only its 117 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. #31774710 | C2 | semidirect |
| 2. #31774706 | C2 | semidirect |
| 3. #31774702 | C2 | semidirect |
| 4. #31774282 | C2 | semidirect |
| 5. #31774168 | C2 | semidirect |
| 6. #31774163 | C2 | semidirect |
| 7. #31774073 | C2 | semidirect |
| 8. #31774072 | C2 | semidirect |
| 9. #31774013 | C2 | semidirect |
| 10. #31774012 | C2 | semidirect |
| 11. #473×C271 | C2 | semidirect |
| 12. #22576208 | C22 | semidirect |
| 16. #22576191 | C22 | semidirect |
| 19. #22576188 | C22 | semidirect |
| 27. C2×#16864641 | C22 | semidirect |
| 31. #22576168 | C22 | semidirect |
| 32. #22576166 | C22 | semidirect |
| 33. #22576149 | C22 | semidirect |
| 34. #22576095 | C22 | semidirect |
| 36. #22576086 | C22 | semidirect |
| 37. #22576086 | C22 | semidirect |
| 38. #22576076 | C22 | semidirect |
| 39. C8×Dic271 | C22 | semidirect |
| 41. C2×Q16×C271 | C22 | semidirect |
| 43. #108×C271 | C22 | semidirect |
| 44. #101×C271 | C22 | semidirect |
| 149. C271 | #3290 | semidirect |
| 155. #473 | D271 | semidirect |
| 178. C2×Q16 | C2×D271 | semidirect |
| 188. #108 | C2×D271 | semidirect |
| 192. #101 | C2×D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774710 | 2 |
| #31774706 | 2 |
| #31774702 | 2 |
| #31774282 | 2 |
| #31774168 | 2 |
| #31774163 | 2 |
| #31774073 | 2 |
| #31774072 | 2 |
| #31774013 | 2 |
| #31774012 | 2 |
| #473×C271 | 2 |
| #3290 | 271 |