Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
556 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 556 conjugacy classes of subgroups — too many to draw. Only its 101 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. C22×#13093965 | C2 | semidirect |
| 2. C2×#15689393 | C2 | semidirect |
| 3. C2×#15688936 | C2 | semidirect |
| 4. C2×#15688935 | C2 | semidirect |
| 5. #20245002 | C2 | semidirect |
| 6. #20241481 | C2 | semidirect |
| 7. C2×C47×#472 | C2 | semidirect |
| 193. C2×#472 | D47 | semidirect |
| 226. C47 | #13313 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13093965 | 2 |
| C2×#15689393 | 2 |
| C2×#15688936 | 2 |
| C2×#15688935 | 2 |
| #20245002 | 2 |
| #20241481 | 2 |
| C2×C47×#472 | 2 |
| #13313 | 47 |