Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
444 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 444 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. #31774712 | C2 | semidirect |
| 2. #31774711 | C2 | semidirect |
| 3. #31774275 | C2 | semidirect |
| 4. #31774172 | C2 | semidirect |
| 5. #31774170 | C2 | semidirect |
| 6. #31774169 | C2 | semidirect |
| 7. #31774080 | C2 | semidirect |
| 8. #31774078 | C2 | semidirect |
| 9. #31774014 | C2 | semidirect |
| 10. #31774012 | C2 | semidirect |
| 11. #578×C271 | C2 | semidirect |
| 146. C271 | #3293 | semidirect |
| 150. #578 | D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774712 | 2 |
| #31774711 | 2 |
| #31774275 | 2 |
| #31774172 | 2 |
| #31774170 | 2 |
| #31774169 | 2 |
| #31774080 | 2 |
| #31774078 | 2 |
| #31774014 | 2 |
| #31774012 | 2 |
| #578×C271 | 2 |
| #3293 | 271 |