Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
852 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 852 conjugacy classes of subgroups — too many to draw. Only its 87 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. #20254195 | C2 | semidirect |
| 2. C2×#15689274 | C2 | semidirect |
| 4. #20241753 | C2 | semidirect |
| 5. #20241749 | C2 | semidirect |
| 6. #20241275 | C2 | semidirect |
| 7. C47×#1783 | C2 | semidirect |
| 227. #1783 | D47 | semidirect |
| 262. C47 | #9987 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20254195 | 2 |
| C2×#15689274 | 2 |
| C2×#15689257 | 2 |
| #20241753 | 2 |
| #20241749 | 2 |
| #20241275 | 2 |
| C47×#1783 | 2 |
| #9987 | 47 |