Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
930 conjugacy classes of subgroups; only the 159 normal subgroups are shown.
This group has 930 conjugacy classes of subgroups — too many to draw. Only its 159 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 |
|---|---|---|
| 1. #20245124 | C2 | semidirect |
| 2. #20245104 | C2 | semidirect |
| 3. #20245009 | C2 | semidirect |
| 4. #20243434 | C2 | semidirect |
| 6. C2×#13093964 | C22 | semidirect |
| 7. #15689161 | C22 | semidirect |
| 18. C2×#135×C47 | C4 | semidirect |
| 20. C22×D8×C47 | C4 | semidirect |
| 185. C2×#135 | Dic47 | semidirect |
| 187. C22×D8 | Dic47 | semidirect |
| 197. C47 | #12741 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20245124 | 2 |
| #20245104 | 2 |
| #20245009 | 2 |
| #20243434 | 2 |
| C2×C47×#576 | 2 |
| #12741 | 47 |