Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
1236 conjugacy classes of subgroups; only the 231 normal subgroups are shown.
This group has 1236 conjugacy classes of subgroups — too many to draw. Only its 231 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. #20251868 | C2 | semidirect |
| 3. #20243937 | C2 | semidirect |
| 4. #20243803 | C2 | semidirect |
| 5. #20243500 | C2 | semidirect |
| 6. #20243312 | C2 | semidirect |
| 7. C47×#1784 | C2 | semidirect |
| 189. #1784 | D47 | semidirect |
| 217. C47 | #21780 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20257039 | 2 |
| #20251868 | 2 |
| #20243937 | 2 |
| #20243803 | 2 |
| #20243500 | 2 |
| #20243312 | 2 |
| C47×#1784 | 2 |
| #21780 | 47 |