Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
456 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 107 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 |
|---|---|---|
| 2. #20243426 | C2 | semidirect |
| 4. #20241294 | C2 | semidirect |
| 5. C47×#1807 | C2 | semidirect |
| 6. C2×#13094030 | C4 | semidirect |
| 13. #15689149 | C4 | semidirect |
| 14. #15689089 | C4 | semidirect |
| 17. #15689078 | C4 | semidirect |
| 180. #1807 | D47 | semidirect |
| 209. C47 | #8626 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20252082 | 2 |
| #20243426 | 2 |
| #20241929 | 2 |
| #20241294 | 2 |
| C47×#1807 | 2 |
| #8626 | 47 |