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 |
|---|---|---|
| 4. #31774183 | C2 | semidirect |
| 5. #31774182 | C2 | semidirect |
| 6. #31774104 | C2 | semidirect |
| 8. #31774004 | C2 | semidirect |
| 9. #31774001 | C2 | semidirect |
| 11. #462×C271 | C2 | semidirect |
| 132. C271 | #3113 | semidirect |
| 140. #462 | D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774452 | 2 |
| C4×Q8×D271 | 2 |
| #31774226 | 2 |
| #31774183 | 2 |
| #31774182 | 2 |
| #31774104 | 2 |
| #31774051 | 2 |
| #31774004 | 2 |
| #31774001 | 2 |
| #31773953 | 2 |
| #462×C271 | 2 |
| #3113 | 271 |