Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
354 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 354 conjugacy classes of subgroups — too many to draw. Only its 125 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. #31774604 | C2 | semidirect |
| 3. #31774302 | C2 | semidirect |
| 4. #31774239 | C2 | semidirect |
| 5. #31774211 | C2 | semidirect |
| 6. #31774193 | C2 | semidirect |
| 7. #31774188 | C2 | semidirect |
| 8. #31774143 | C2 | semidirect |
| 9. C4×#16864643 | C2 | semidirect |
| 10. #31773939 | C2 | semidirect |
| 11. #436×C271 | C2 | semidirect |
| 121. C271 | #3357 | semidirect |
| 132. #436 | D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774612 | 2 |
| #31774604 | 2 |
| #31774302 | 2 |
| #31774239 | 2 |
| #31774211 | 2 |
| #31774193 | 2 |
| #31774188 | 2 |
| #31774143 | 2 |
| C4×#16864643 | 2 |
| #31773939 | 2 |
| #436×C271 | 2 |
| #3357 | 271 |