Finite Group DatabasebetaFinite Group DatabasebetaOrder 2752.
104 conjugacy classes of subgroups; only the 37 normal subgroups are shown.
This group has 104 conjugacy classes of subgroups — too many to draw. Only its 37 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. #13063358 | C2 | semidirect |
| 3. C2×#10621873 | C2 | semidirect |
| 4. #13063331 | C2 | semidirect |
| 5. #13063243 | C2 | semidirect |
| 6. #13063241 | C2 | semidirect |
| 7. #108×C43 | C2 | semidirect |
| 52. C43 | #471 | semidirect |
| 57. #108 | D43 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13063358 | 2 |
| #13063353 | 2 |
| C2×#10621873 | 2 |
| #13063331 | 2 |
| #13063243 | 2 |
| #13063241 | 2 |
| #108×C43 | 2 |
| #471 | 43 |