Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
364 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 364 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. #31774454 | C2 | semidirect |
| 2. #31774307 | C2 | semidirect |
| 3. #31774292 | C2 | semidirect |
| 4. #31774267 | C2 | semidirect |
| 5. #31774256 | C2 | semidirect |
| 6. #31774153 | C2 | semidirect |
| 8. C4×#16864644 | C2 | semidirect |
| 9. C4×#16864642 | C2 | semidirect |
| 10. C4×#16864638 | C2 | semidirect |
| 129. C271 | #3172 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774454 | 2 |
| #31774307 | 2 |
| #31774292 | 2 |
| #31774267 | 2 |
| #31774256 | 2 |
| #31774153 | 2 |
| #31774141 | 2 |
| C4×#16864644 | 2 |
| C4×#16864642 | 2 |
| C4×#16864638 | 2 |
| #529×C271 | 2 |
| #3172 | 271 |