Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
356 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 356 conjugacy classes of subgroups — too many to draw. Only its 99 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. #20244161 | C2 | semidirect |
| 5. #20241678 | C2 | semidirect |
| 6. #20241229 | C2 | semidirect |
| 7. C47×#1303 | C2 | semidirect |
| 16. #15688868 | C4 | semidirect |
| 17. #15688868 | C4 | semidirect |
| 18. #15688866 | C4 | semidirect |
| 19. #15688866 | C4 | semidirect |
| 169. #1303 | D47 | semidirect |
| 196. C47 | #9592 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20244306 | 2 |
| #20244161 | 2 |
| #20242035 | 2 |
| #20241838 | 2 |
| #20241678 | 2 |
| #20241229 | 2 |
| C47×#1303 | 2 |
| #9592 | 47 |