Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
106 conjugacy classes of subgroups; only the 23 normal subgroups are shown.
This group has 106 conjugacy classes of subgroups — too many to draw. Only its 23 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. #31773696 | C2 | semidirect |
| 3. #333×C271 | C2 | semidirect |
| 51. C271 | #1405 | semidirect |
| 55. #333 | D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774079 | 2 |
| #31773696 | 2 |
| #333×C271 | 2 |
| #1405 | 271 |