Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
336 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 113 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. #31774240 | C2 | semidirect |
| 3. #31774234 | C2 | semidirect |
| 4. #31774201 | C2 | semidirect |
| 5. #31774156 | C2 | semidirect |
| 6. C4×Dic1084 | C2 | semidirect |
| 8. #31773936 | C2 | semidirect |
| 9. #499×C271 | C2 | semidirect |
| 96. C271 | #3352 | semidirect |
| 99. #499 | D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774585 | 2 |
| #31774240 | 2 |
| #31774234 | 2 |
| #31774201 | 2 |
| #31774156 | 2 |
| C4×Dic1084 | 2 |
| #31773976 | 2 |
| #31773936 | 2 |
| #499×C271 | 2 |
| #3352 | 271 |