Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
716 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 716 conjugacy classes of subgroups — too many to draw. Only its 145 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. #31774473 | C2 | semidirect |
| 3. #31774468 | C2 | semidirect |
| 4. #31774088 | C2 | semidirect |
| 5. #31773870 | C2 | semidirect |
| 6. #410×C271 | C2 | semidirect |
| 15. C22×Dic542 | C22 | semidirect |
| 20. #22576144 | C22 | semidirect |
| 21. #22576141 | C22 | semidirect |
| 24. #22576119 | C22 | semidirect |
| 25. #22576074 | C22 | semidirect |
| 27. #117×C271 | C22 | semidirect |
| 28. #99×C271 | C22 | semidirect |
| 128. C271 | #3028 | semidirect |
| 135. #410 | D271 | semidirect |
| 155. #117 | C2×D271 | semidirect |
| 157. #99 | C2×D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774733 | 2 |
| #31774473 | 2 |
| #31774468 | 2 |
| #31774088 | 2 |
| #31773870 | 2 |
| #410×C271 | 2 |
| #3028 | 271 |