Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
380 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 121 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. #31774433 | C2 | semidirect |
| 2. #31774298 | C2 | semidirect |
| 3. #31774282 | C2 | semidirect |
| 4. #31774253 | C2 | semidirect |
| 6. #31774128 | C2 | semidirect |
| 7. Q16×Dic271 | C2 | semidirect |
| 8. #31773982 | C2 | semidirect |
| 9. #31773979 | C2 | semidirect |
| 10. C2×C8×Dic271 | C2 | semidirect |
| 11. #467×C271 | C2 | semidirect |
| 118. C271 | #3168 | semidirect |
| 124. #467 | D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774433 | 2 |
| #31774298 | 2 |
| #31774282 | 2 |
| #31774253 | 2 |
| #31774133 | 2 |
| #31774128 | 2 |
| Q16×Dic271 | 2 |
| #31773982 | 2 |
| #31773979 | 2 |
| C2×C8×Dic271 | 2 |
| #467×C271 | 2 |
| #3168 | 271 |