Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
396 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 125 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. #31774617 | C2 | semidirect |
| 2. #31774243 | C2 | semidirect |
| 3. #31774218 | C2 | semidirect |
| 4. #31774182 | C2 | semidirect |
| 5. #31774124 | C2 | semidirect |
| 6. #31774094 | C2 | semidirect |
| 7. #31774059 | C2 | semidirect |
| 8. C4×#16864644 | C2 | semidirect |
| 9. D4×C271⋊C8 | C2 | semidirect |
| 10. #31773893 | C2 | semidirect |
| 127. C271 | #3304 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774617 | 2 |
| #31774243 | 2 |
| #31774218 | 2 |
| #31774182 | 2 |
| #31774124 | 2 |
| #31774094 | 2 |
| #31774059 | 2 |
| C4×#16864644 | 2 |
| D4×C271⋊C8 | 2 |
| #31773893 | 2 |
| #550×C271 | 2 |
| #3304 | 271 |