Finite Group DatabasebetaFinite Group DatabasebetaOrder 2752.
146 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 146 conjugacy classes of subgroups — too many to draw. Only its 39 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. #13063372 | C2 | semidirect |
| 2. #13063353 | C2 | semidirect |
| 3. #13063350 | C2 | semidirect |
| 4. #13063313 | C2 | semidirect |
| 5. #13063253 | C2 | semidirect |
| 6. #13063243 | C2 | semidirect |
| 7. #104×C43 | C2 | semidirect |
| 64. C43 | #454 | semidirect |
| 70. #104 | D43 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13063372 | 2 |
| #13063353 | 2 |
| #13063350 | 2 |
| #13063313 | 2 |
| #13063253 | 2 |
| #13063243 | 2 |
| #104×C43 | 2 |
| #454 | 43 |