Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
424 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 121 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 |
|---|---|---|
| 2. C4⋊Q8×D271 | C2 | semidirect |
| 3. #31774259 | C2 | semidirect |
| 4. #31774257 | C2 | semidirect |
| 5. #31774256 | C2 | semidirect |
| 6. #31774246 | C2 | semidirect |
| 7. #31774242 | C2 | semidirect |
| 8. #31773897 | C2 | semidirect |
| 9. #31773895 | C2 | semidirect |
| 10. #31773849 | C2 | semidirect |
| 11. #489×C271 | C2 | semidirect |
| 140. C271 | #3141 | semidirect |
| 147. #489 | D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774446 | 2 |
| C4⋊Q8×D271 | 2 |
| #31774259 | 2 |
| #31774257 | 2 |
| #31774256 | 2 |
| #31774246 | 2 |
| #31774242 | 2 |
| #31773897 | 2 |
| #31773895 | 2 |
| #31773849 | 2 |
| #489×C271 | 2 |
| #3141 | 271 |