Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
498 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 498 conjugacy classes of subgroups — too many to draw. Only its 111 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. #20244307 | C2 | semidirect |
| 3. C4×#13093955 | C2 | semidirect |
| 4. #20241883 | C2 | semidirect |
| 5. #20241882 | C2 | semidirect |
| 6. #20241675 | C2 | semidirect |
| 7. C47×#1980 | C2 | semidirect |
| 9. #15689526 | C4 | semidirect |
| 10. #15689499 | C4 | semidirect |
| 11. #15689471 | C4 | semidirect |
| 12. #15689469 | C4 | semidirect |
| 171. C47⋊C8 | #104 | semidirect |
| 197. #1980 | D47 | semidirect |
| 232. C47 | #9721 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20253963 | 2 |
| #20244307 | 2 |
| C4×#13093955 | 2 |
| #20241883 | 2 |
| #20241882 | 2 |
| #20241675 | 2 |
| C47×#1980 | 2 |
| #9721 | 47 |