Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
386 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 117 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. #31774620 | C2 | semidirect |
| 3. #31774248 | C2 | semidirect |
| 4. #31774241 | C2 | semidirect |
| 5. #31774177 | C2 | semidirect |
| 6. #31774137 | C2 | semidirect |
| 7. #31774107 | C2 | semidirect |
| 8. #31774056 | C2 | semidirect |
| 9. C8×D1084 | C2 | semidirect |
| 10. #31773890 | C2 | semidirect |
| 11. C4×SD16×C271 | C2 | semidirect |
| 125. C271 | #3302 | semidirect |
| 135. C4×SD16 | D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774620 | 2 |
| #31774551 | 2 |
| #31774248 | 2 |
| #31774241 | 2 |
| #31774177 | 2 |
| #31774137 | 2 |
| #31774107 | 2 |
| #31774056 | 2 |
| C8×D1084 | 2 |
| #31773890 | 2 |
| C4×SD16×C271 | 2 |
| #3302 | 271 |