Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
386 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 119 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. #31774452 | C2 | semidirect |
| 3. #31774237 | C2 | semidirect |
| 4. #31774193 | C2 | semidirect |
| 5. #31774187 | C2 | semidirect |
| 6. #31774104 | C2 | semidirect |
| 8. #31774001 | C2 | semidirect |
| 9. #31773998 | C2 | semidirect |
| 10. #31773953 | C2 | semidirect |
| 11. #461×C271 | C2 | semidirect |
| 136. C271 | #3116 | semidirect |
| 144. #461 | D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774452 | 2 |
| C4×#16864653 | 2 |
| #31774237 | 2 |
| #31774193 | 2 |
| #31774187 | 2 |
| #31774104 | 2 |
| #31774056 | 2 |
| #31774001 | 2 |
| #31773998 | 2 |
| #31773953 | 2 |
| #461×C271 | 2 |
| #3116 | 271 |