Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
362 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 362 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 |
|---|---|---|
| 1. #31774509 | C2 | semidirect |
| 3. #31774299 | C2 | semidirect |
| 4. #31774270 | C2 | semidirect |
| 5. #31774266 | C2 | semidirect |
| 6. #31774262 | C2 | semidirect |
| 7. #31774143 | C2 | semidirect |
| 8. #31774126 | C2 | semidirect |
| 9. #31773999 | C2 | semidirect |
| 10. C4×#16864643 | C2 | semidirect |
| 11. #405×C271 | C2 | semidirect |
| 108. C271 | #3174 | semidirect |
| 120. #405 | D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774509 | 2 |
| #31774502 | 2 |
| #31774299 | 2 |
| #31774270 | 2 |
| #31774266 | 2 |
| #31774262 | 2 |
| #31774143 | 2 |
| #31774126 | 2 |
| #31773999 | 2 |
| C4×#16864643 | 2 |
| #405×C271 | 2 |
| #3174 | 271 |