Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
484 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 129 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. #31774450 | C2 | semidirect |
| 3. #31774260 | C2 | semidirect |
| 4. #31774242 | C2 | semidirect |
| 5. #31773903 | C2 | semidirect |
| 6. #31773902 | C2 | semidirect |
| 7. #31773901 | C2 | semidirect |
| 8. M16×Dic271 | C2 | semidirect |
| 9. #418×C271 | C2 | semidirect |
| 13. #22576159 | C22 | semidirect |
| 17. #22576151 | C22 | semidirect |
| 22. #22576082 | C22 | semidirect |
| 23. #22576081 | C22 | semidirect |
| 24. #22576080 | C22 | semidirect |
| 25. #22576070 | C22 | semidirect |
| 26. C8×Dic271 | C22 | semidirect |
| 30. #102×C271 | C22 | semidirect |
| 111. C271 | #3138 | semidirect |
| 120. #418 | D271 | semidirect |
| 140. #102 | C2×D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774450 | 2 |
| C2×#22576156 | 2 |
| #31774260 | 2 |
| #31774242 | 2 |
| #31773903 | 2 |
| #31773902 | 2 |
| #31773901 | 2 |
| M16×Dic271 | 2 |
| #418×C271 | 2 |
| #3138 | 271 |