Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
238 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 238 conjugacy classes of subgroups — too many to draw. Only its 63 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. #31773947 | C2 | semidirect |
| 3. #31773742 | C2 | semidirect |
| 4. #31773634 | C2 | semidirect |
| 7. #328×C271 | C2 | semidirect |
| 9. #22576151 | C4 | semidirect |
| 10. #22576149 | C4 | semidirect |
| 13. Q8×Dic271 | C4 | semidirect |
| 14. #22576122 | C4 | semidirect |
| 108. C271 | #1500 | semidirect |
| 114. #328 | D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774433 | 2 |
| #31773947 | 2 |
| #31773742 | 2 |
| #31773634 | 2 |
| #31773632 | 2 |
| #31773630 | 2 |
| #328×C271 | 2 |
| #1500 | 271 |