Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
1128 conjugacy classes of subgroups; only the 351 normal subgroups are shown.
This group has 1128 conjugacy classes of subgroups — too many to draw. Only its 351 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. #20256491 | C2 | semidirect |
| 3. #20245123 | C2 | semidirect |
| 4. C2×#15688932 | C2 | semidirect |
| 5. C47×#2912 | C2 | semidirect |
| 7. #15689940 | C4 | semidirect |
| 9. #15689928 | C4 | semidirect |
| 13. C2×#13093964 | C22 | semidirect |
| 14. #15688932 | C22 | semidirect |
| 15. #15688932 | C22 | semidirect |
| 19. C47×#427 | C22 | semidirect |
| 20. C2×#106×C47 | C22 | semidirect |
| 31. #13094046 | C2×C4 | semidirect |
| 33. C2×Dic188 | C2×C4 | semidirect |
| 35. C2×D376 | C2×C4 | semidirect |
| 124. #2912 | D47 | semidirect |
| 142. #427 | C2×D47 | semidirect |
| 143. C2×#106 | C2×D47 | semidirect |
| 146. C47 | #33388 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20258162 | 2 |
| #20256491 | 2 |
| #20245123 | 2 |
| C2×#15688932 | 2 |
| C47×#2912 | 2 |
| #33388 | 47 |