Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
384 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 115 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. #31774632 | C2 | semidirect |
| 2. #31774562 | C2 | semidirect |
| 3. #31774258 | C2 | semidirect |
| 4. #31774245 | C2 | semidirect |
| 5. #31774186 | C2 | semidirect |
| 6. #31774115 | C2 | semidirect |
| 8. #31774024 | C2 | semidirect |
| 9. #31774008 | C2 | semidirect |
| 10. C4×#16864641 | C2 | semidirect |
| 11. #475×C271 | C2 | semidirect |
| 124. C271 | #3373 | semidirect |
| 131. #475 | D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774632 | 2 |
| #31774562 | 2 |
| #31774258 | 2 |
| #31774245 | 2 |
| #31774186 | 2 |
| #31774115 | 2 |
| #31774093 | 2 |
| #31774024 | 2 |
| #31774008 | 2 |
| C4×#16864641 | 2 |
| #475×C271 | 2 |
| #3373 | 271 |