Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
478 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 478 conjugacy classes of subgroups — too many to draw. Only its 99 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 |
|---|---|---|
| 3. #20244364 | C2 | semidirect |
| 5. #20241810 | C2 | semidirect |
| 6. #20241220 | C2 | semidirect |
| 7. C47×#1299 | C2 | semidirect |
| 11. #15689409 | C4 | semidirect |
| 12. #15689404 | C4 | semidirect |
| 13. #15689334 | C4 | semidirect |
| 14. #15689329 | C4 | semidirect |
| 206. #1299 | D47 | semidirect |
| 238. C47 | #8971 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20253460 | 2 |
| #20252514 | 2 |
| #20244364 | 2 |
| C4×#13093950 | 2 |
| #20241810 | 2 |
| #20241220 | 2 |
| C47×#1299 | 2 |
| #8971 | 47 |