Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
372 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 372 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. #31774528 | C2 | semidirect |
| 3. #31774264 | C2 | semidirect |
| 4. #31774258 | C2 | semidirect |
| 5. #31774253 | C2 | semidirect |
| 6. #31774246 | C2 | semidirect |
| 7. #31773906 | C2 | semidirect |
| 10. #31773852 | C2 | semidirect |
| 11. C2×#103×C271 | C2 | semidirect |
| 127. C271 | #3137 | semidirect |
| 138. C2×#103 | D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774528 | 2 |
| #31774471 | 2 |
| #31774264 | 2 |
| #31774258 | 2 |
| #31774253 | 2 |
| #31774246 | 2 |
| #31773906 | 2 |
| #31773896 | 2 |
| #31773894 | 2 |
| #31773852 | 2 |
| C2×#103×C271 | 2 |
| #3137 | 271 |