Finite Group DatabasebetaFinite Group DatabasebetaOrder 2752.
234 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 101 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. #13063320 | C2 | semidirect |
| 2. #13063318 | C2 | semidirect |
| 3. #13063315 | C2 | semidirect |
| 4. #13063311 | C2 | semidirect |
| 5. #13063309 | C2 | semidirect |
| 6. #13063306 | C2 | semidirect |
| 7. #13063302 | C2 | semidirect |
| 9. C4×Dic86 | C2 | semidirect |
| 10. C4×C22⋊D43 | C2 | semidirect |
| 11. C4×C22⋊D43 | C2 | semidirect |
| 12. #13063284 | C2 | semidirect |
| 13. #13063282 | C2 | semidirect |
| 14. C2×C4×Dic43 | C2 | semidirect |
| 15. C4×D4×C43 | C2 | semidirect |
| 104. C43 | #529 | semidirect |
| 116. C4×D4 | D43 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13063320 | 2 |
| #13063318 | 2 |
| #13063315 | 2 |
| #13063311 | 2 |
| #13063309 | 2 |
| #13063306 | 2 |
| #13063302 | 2 |
| #13063297 | 2 |
| C4×Dic86 | 2 |
| C4×C22⋊D43 | 2 |
| #13063284 | 2 |
| #13063282 | 2 |
| C2×C4×Dic43 | 2 |
| C4×D4×C43 | 2 |
| #529 | 43 |