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. #13063318 | C2 | semidirect |
| 2. #13063316 | C2 | semidirect |
| 3. #13063312 | C2 | semidirect |
| 4. #13063307 | C2 | semidirect |
| 5. #13063305 | C2 | semidirect |
| 7. C4×Dic86 | C2 | semidirect |
| 8. C4×C22⋊D43 | C2 | semidirect |
| 9. #13063284 | C2 | semidirect |
| 10. C42×D43 | C2 | semidirect |
| 11. C4×D4×C43 | C2 | semidirect |
| 75. C43 | #529 | semidirect |
| 84. C4×D4 | D43 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13063318 | 2 |
| #13063316 | 2 |
| #13063312 | 2 |
| #13063307 | 2 |
| #13063305 | 2 |
| #13063296 | 2 |
| C4×Dic86 | 2 |
| C4×C22⋊D43 | 2 |
| #13063284 | 2 |
| C42×D43 | 2 |
| C4×D4×C43 | 2 |
| #529 | 43 |