Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
1078 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 1078 conjugacy classes of subgroups — too many to draw. Only its 171 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. #20254383 | C2 | semidirect |
| 2. #20253833 | C2 | semidirect |
| 3. #20242694 | C2 | semidirect |
| 4. #20242677 | C2 | semidirect |
| 5. #20242023 | C2 | semidirect |
| 6. #20241999 | C2 | semidirect |
| 7. C47×#3549 | C2 | semidirect |
| 9. #15689673 | C22 | semidirect |
| 10. #15689518 | C22 | semidirect |
| 12. #15689513 | C22 | semidirect |
| 13. #15689513 | C22 | semidirect |
| 15. #15689482 | C22 | semidirect |
| 19. #15689180 | C22 | semidirect |
| 20. C2×#13093935 | C22 | semidirect |
| 21. #15688863 | C22 | semidirect |
| 22. #15688863 | C22 | semidirect |
| 185. #3549 | D47 | semidirect |
| 222. C47 | #19052 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20254383 | 2 |
| #20253833 | 2 |
| #20242694 | 2 |
| #20242677 | 2 |
| #20242023 | 2 |
| #20241999 | 2 |
| C47×#3549 | 2 |
| #19052 | 47 |