Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
496 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 496 conjugacy classes of subgroups — too many to draw. Only its 83 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. #20249509 | C2 | semidirect |
| 4. #20242106 | C2 | semidirect |
| 6. #20241282 | C2 | semidirect |
| 7. C47×#1528 | C2 | semidirect |
| 173. #1528 | D47 | semidirect |
| 204. C47 | #10093 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20254578 | 2 |
| #20253782 | 2 |
| #20249509 | 2 |
| #20242106 | 2 |
| #20241897 | 2 |
| #20241282 | 2 |
| C47×#1528 | 2 |
| #10093 | 47 |