Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
256 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 57 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. #31774271 | C2 | semidirect |
| 3. #31774184 | C2 | semidirect |
| 4. #31773640 | C2 | semidirect |
| 5. Q8⋊(C271⋊C8) | C2 | semidirect |
| 6. #31773624 | C2 | semidirect |
| 7. #477×C271 | C2 | semidirect |
| 69. Q8×C271 | SD16 | semidirect |
| 98. C271 | #1631 | semidirect |
| 102. #477 | D271 | semidirect |
| 153. Q8 | #16864641 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774569 | 2 |
| #31774271 | 2 |
| #31774184 | 2 |
| #31773640 | 2 |
| Q8⋊(C271⋊C8) | 2 |
| #31773624 | 2 |
| #477×C271 | 2 |
| #1631 | 271 |