Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
336 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 336 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. #31774622 | C2 | semidirect |
| 4. #31774202 | C2 | semidirect |
| 7. #31774104 | C2 | semidirect |
| 8. C8×Dic542 | C2 | semidirect |
| 9. #31773989 | C2 | semidirect |
| 11. #487×C271 | C2 | semidirect |
| 115. C271 | #3364 | semidirect |
| 120. #487 | D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774622 | 2 |
| #31774621 | 2 |
| #31774253 | 2 |
| #31774202 | 2 |
| #31774174 | 2 |
| #31774122 | 2 |
| #31774104 | 2 |
| C8×Dic542 | 2 |
| #31773989 | 2 |
| C4×#16864643 | 2 |
| #487×C271 | 2 |
| #3364 | 271 |