Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
168 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 168 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 |
|---|---|---|
| 2. #31774183 | C2 | semidirect |
| 4. #31774024 | C2 | semidirect |
| 5. #31773649 | C2 | semidirect |
| 6. #31773644 | C2 | semidirect |
| 51. C271⋊C8 | SD16 | semidirect |
| 79. C271 | #1686 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774269 | 2 |
| #31774183 | 2 |
| #31774094 | 2 |
| #31774024 | 2 |
| #31773649 | 2 |
| #31773644 | 2 |
| #331×C271 | 2 |
| #1686 | 271 |