Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
590 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 590 conjugacy classes of subgroups — too many to draw. Only its 85 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. #20253782 | C2 | semidirect |
| 3. #20249498 | C2 | semidirect |
| 4. #20242106 | C2 | semidirect |
| 5. #20241985 | C2 | semidirect |
| 6. #20241895 | C2 | semidirect |
| 7. C47×#1300 | C2 | semidirect |
| 193. #1300 | D47 | semidirect |
| 223. C47 | #10094 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20254377 | 2 |
| #20253782 | 2 |
| #20249498 | 2 |
| #20242106 | 2 |
| #20241985 | 2 |
| #20241895 | 2 |
| C47×#1300 | 2 |
| #10094 | 47 |