Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
142 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 142 conjugacy classes of subgroups — too many to draw. Only its 51 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. #31774301 | C2 | semidirect |
| 3. #31773725 | C2 | semidirect |
| 4. #31773724 | C2 | semidirect |
| 5. Dic271⋊C16 | C2 | semidirect |
| 30. D8×C271 | Q8 | semidirect |
| 63. C271 | #2226 | semidirect |
| 87. D8 | Dic542 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774301 | 2 |
| D8×Dic271 | 2 |
| #31773725 | 2 |
| #31773724 | 2 |
| Dic271⋊C16 | 2 |
| #31773698 | 2 |
| #357×C271 | 2 |
| #2226 | 271 |