Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
372 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 372 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. #31774525 | C2 | semidirect |
| 3. #31774266 | C2 | semidirect |
| 4. #31774257 | C2 | semidirect |
| 5. #31774252 | C2 | semidirect |
| 6. #31774248 | C2 | semidirect |
| 7. #31773907 | C2 | semidirect |
| 10. C2×#22576085 | C2 | semidirect |
| 11. #405×C271 | C2 | semidirect |
| 127. C271 | #3137 | semidirect |
| 139. #405 | D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774525 | 2 |
| #31774473 | 2 |
| #31774266 | 2 |
| #31774257 | 2 |
| #31774252 | 2 |
| #31774248 | 2 |
| #31773907 | 2 |
| #31773899 | 2 |
| #31773894 | 2 |
| C2×#22576085 | 2 |
| #405×C271 | 2 |
| #3137 | 271 |