Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
406 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 406 conjugacy classes of subgroups — too many to draw. Only its 105 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. #20245162 | C2 | semidirect |
| 5. #20241489 | C2 | semidirect |
| 6. #20241470 | C2 | semidirect |
| 7. C47×#1945 | C2 | semidirect |
| 20. #15688932 | C4 | semidirect |
| 43. #13093964 | C2×C4 | semidirect |
| 58. #106×C47 | C2×C4 | semidirect |
| 154. #1945 | D47 | semidirect |
| 180. C47 | #12951 | semidirect |
| 211. #106 | C4×D47 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#13094046 | 2 |
| #20245162 | 2 |
| #20245135 | 2 |
| #20245123 | 2 |
| #20241489 | 2 |
| #20241470 | 2 |
| C47×#1945 | 2 |
| #12951 | 47 |