Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
374 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 374 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. #20244163 | C2 | semidirect |
| 3. #20242163 | C2 | semidirect |
| 6. #20241263 | C2 | semidirect |
| 7. C47×#1565 | C2 | semidirect |
| 155. #1565 | D47 | semidirect |
| 182. C47 | #10603 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20244228 | 2 |
| #20244163 | 2 |
| #20242163 | 2 |
| #20242055 | 2 |
| C2×#15688866 | 2 |
| #20241263 | 2 |
| C47×#1565 | 2 |
| #10603 | 47 |