Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
348 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 75 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. #20243529 | C2 | semidirect |
| 3. #20242118 | C2 | semidirect |
| 6. #20241298 | C2 | semidirect |
| 7. C47×#1531 | C2 | semidirect |
| 153. #1531 | D47 | semidirect |
| 180. C47 | #10527 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20254771 | 2 |
| #20243529 | 2 |
| #20242118 | 2 |
| #20242111 | 2 |
| #20241998 | 2 |
| #20241298 | 2 |
| C47×#1531 | 2 |
| #10527 | 47 |