Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
392 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 392 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. #31774453 | C2 | semidirect |
| 3. #31774267 | C2 | semidirect |
| 4. #31774266 | C2 | semidirect |
| 5. #31774261 | C2 | semidirect |
| 6. #31774255 | C2 | semidirect |
| 7. #31773890 | C2 | semidirect |
| 8. #97×D271 | C2 | semidirect |
| 9. #490×C271 | C2 | semidirect |
| 90. C271 | #3135 | semidirect |
| 97. #490 | D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774453 | 2 |
| #31774445 | 2 |
| #31774267 | 2 |
| #31774266 | 2 |
| #31774261 | 2 |
| #31774255 | 2 |
| #31773890 | 2 |
| #97×D271 | 2 |
| #490×C271 | 2 |
| #3135 | 271 |