Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
400 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 133 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. #31774454 | C2 | semidirect |
| 2. #31774256 | C2 | semidirect |
| 3. #31774251 | C2 | semidirect |
| 4. #31773906 | C2 | semidirect |
| 6. C4×#16864638 | C2 | semidirect |
| 9. #22576160 | C22 | semidirect |
| 10. #22576152 | C22 | semidirect |
| 14. #22576084 | C22 | semidirect |
| 16. #22576071 | C22 | semidirect |
| 17. C4×C271⋊C8 | C22 | semidirect |
| 83. C271 | #3140 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774454 | 2 |
| #31774256 | 2 |
| #31774251 | 2 |
| #31773906 | 2 |
| #31773902 | 2 |
| C4×#16864638 | 2 |
| C2×#124×C271 | 2 |
| #3140 | 271 |