Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
362 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 362 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. #31774521 | C2 | semidirect |
| 2. #31774281 | C2 | semidirect |
| 3. #31774259 | C2 | semidirect |
| 4. #31774144 | C2 | semidirect |
| 5. #31774139 | C2 | semidirect |
| 7. #31773996 | C2 | semidirect |
| 8. #31773991 | C2 | semidirect |
| 9. #31773979 | C2 | semidirect |
| 10. #31773851 | C2 | semidirect |
| 11. #500×C271 | C2 | semidirect |
| 117. C271 | #3175 | semidirect |
| 120. #500 | D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774521 | 2 |
| #31774281 | 2 |
| #31774259 | 2 |
| #31774144 | 2 |
| #31774139 | 2 |
| #31774134 | 2 |
| #31773996 | 2 |
| #31773991 | 2 |
| #31773979 | 2 |
| #31773851 | 2 |
| #500×C271 | 2 |
| #3175 | 271 |