Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
992 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 992 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. #20254399 | C2 | semidirect |
| 2. #20253733 | C2 | semidirect |
| 3. #20242694 | C2 | semidirect |
| 4. #20242023 | C2 | semidirect |
| 5. #20241999 | C2 | semidirect |
| 7. #15689680 | C22 | semidirect |
| 8. #15689518 | C22 | semidirect |
| 11. #15689482 | C22 | semidirect |
| 12. #15689482 | C22 | semidirect |
| 16. #15689180 | C22 | semidirect |
| 18. C2×#13093935 | C22 | semidirect |
| 19. #15688863 | C22 | semidirect |
| 20. #15688863 | C22 | semidirect |
| 200. C47 | #19056 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20254399 | 2 |
| #20253733 | 2 |
| #20242694 | 2 |
| #20242023 | 2 |
| #20241999 | 2 |
| C47×#3549 | 2 |
| #19056 | 47 |