Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
456 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 89 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. #20252466 | C2 | semidirect |
| 3. #20241897 | C2 | semidirect |
| 4. #20241897 | C2 | semidirect |
| 5. #20241856 | C2 | semidirect |
| 6. #20241216 | C2 | semidirect |
| 7. C47×#1287 | C2 | semidirect |
| 10. #15689500 | C4 | semidirect |
| 11. #15689496 | C4 | semidirect |
| 12. #15689474 | C4 | semidirect |
| 13. #15689470 | C4 | semidirect |
| 178. #1287 | D47 | semidirect |
| 207. C47 | #9281 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20254323 | 2 |
| #20252466 | 2 |
| #20241897 | 2 |
| #20241856 | 2 |
| #20241216 | 2 |
| C47×#1287 | 2 |
| #9281 | 47 |