Finite Group DatabasebetaFinite Group DatabasebetaOrder 2752.
234 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 103 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. #13063319 | C2 | semidirect |
| 2. #13063317 | C2 | semidirect |
| 3. #13063313 | C2 | semidirect |
| 4. #13063308 | C2 | semidirect |
| 5. #13063304 | C2 | semidirect |
| 7. C4×Dic86 | C2 | semidirect |
| 8. C4×D172 | C2 | semidirect |
| 9. C4×C22⋊D43 | C2 | semidirect |
| 10. #13063282 | C2 | semidirect |
| 11. C2×C42×C43 | C2 | semidirect |
| 75. C43 | #529 | semidirect |
| 86. C2×C42 | D43 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13063319 | 2 |
| #13063317 | 2 |
| #13063313 | 2 |
| #13063308 | 2 |
| #13063304 | 2 |
| #13063299 | 2 |
| C4×Dic86 | 2 |
| C4×D172 | 2 |
| C4×C22⋊D43 | 2 |
| #13063282 | 2 |
| C2×C42×C43 | 2 |
| #529 | 43 |