Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
458 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 458 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 |
|---|---|---|
| 3. #20242074 | C2 | semidirect |
| 4. #20242072 | C2 | semidirect |
| 6. #20241246 | C2 | semidirect |
| 7. C47×#1286 | C2 | semidirect |
| 188. #1286 | D47 | semidirect |
| 216. C47 | #9194 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20252025 | 2 |
| #20249212 | 2 |
| #20242074 | 2 |
| #20242072 | 2 |
| #20241700 | 2 |
| #20241246 | 2 |
| C47×#1286 | 2 |
| #9194 | 47 |