Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
472 conjugacy classes of subgroups; only the 151 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 151 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. #20256529 | C2 | semidirect |
| 2. #20245701 | C2 | semidirect |
| 3. #20245700 | C2 | semidirect |
| 4. #20245695 | C2 | semidirect |
| 5. C2×#15688958 | C2 | semidirect |
| 6. #20245682 | C2 | semidirect |
| 7. C47×#3415 | C2 | semidirect |
| 10. #15689555 | C22 | semidirect |
| 11. C2×D752 | C22 | semidirect |
| 12. #15688963 | C22 | semidirect |
| 13. #15688961 | C22 | semidirect |
| 14. #15688960 | C22 | semidirect |
| 15. #15688958 | C22 | semidirect |
| 16. #15688958 | C22 | semidirect |
| 17. #15688957 | C22 | semidirect |
| 18. C2×C47⋊C32 | C22 | semidirect |
| 21. C47×#508 | C22 | semidirect |
| 22. C2×D16×C47 | C22 | semidirect |
| 94. #3415 | D47 | semidirect |
| 109. #508 | C2×D47 | semidirect |
| 111. C2×D16 | C2×D47 | semidirect |
| 120. C47 | #33982 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20256529 | 2 |
| #20245701 | 2 |
| #20245700 | 2 |
| #20245695 | 2 |
| C2×#15688958 | 2 |
| #20245682 | 2 |
| C47×#3415 | 2 |
| #33982 | 47 |