Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
404 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 404 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. #31774525 | C2 | semidirect |
| 3. #31774260 | C2 | semidirect |
| 4. #31774255 | C2 | semidirect |
| 5. #31774250 | C2 | semidirect |
| 6. #31774242 | C2 | semidirect |
| 7. #31773899 | C2 | semidirect |
| 8. #31773891 | C2 | semidirect |
| 9. C2×#22576081 | C2 | semidirect |
| 10. #31773855 | C2 | semidirect |
| 11. #418×C271 | C2 | semidirect |
| 15. #22576159 | C22 | semidirect |
| 18. #22576151 | C22 | semidirect |
| 26. #22576085 | C22 | semidirect |
| 27. #22576083 | C22 | semidirect |
| 28. #22576083 | C22 | semidirect |
| 29. #22576082 | C22 | semidirect |
| 32. #22576080 | C22 | semidirect |
| 33. #22576080 | C22 | semidirect |
| 34. #22576070 | C22 | semidirect |
| 35. C8×Dic271 | C22 | semidirect |
| 135. C271 | #3136 | semidirect |
| 143. #418 | D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774525 | 2 |
| #31774464 | 2 |
| #31774260 | 2 |
| #31774255 | 2 |
| #31774250 | 2 |
| #31774242 | 2 |
| #31773899 | 2 |
| #31773891 | 2 |
| C2×#22576081 | 2 |
| #31773855 | 2 |
| #418×C271 | 2 |
| #3136 | 271 |