Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
362 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 362 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. #31774512 | C2 | semidirect |
| 2. #31774301 | C2 | semidirect |
| 3. #31774280 | C2 | semidirect |
| 4. #31774255 | C2 | semidirect |
| 5. #31774142 | C2 | semidirect |
| 6. #31774139 | C2 | semidirect |
| 8. #31773997 | C2 | semidirect |
| 9. C4×Dic1084 | C2 | semidirect |
| 10. #31773851 | C2 | semidirect |
| 11. C4×D8×C271 | C2 | semidirect |
| 117. C271 | #3175 | semidirect |
| 128. C4×D8 | D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774512 | 2 |
| #31774301 | 2 |
| #31774280 | 2 |
| #31774255 | 2 |
| #31774142 | 2 |
| #31774139 | 2 |
| #31774130 | 2 |
| #31773997 | 2 |
| C4×Dic1084 | 2 |
| #31773851 | 2 |
| C4×D8×C271 | 2 |
| #3175 | 271 |