Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
628 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 628 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 |
|---|---|---|
| 1. #20254580 | C2 | semidirect |
| 3. #20249333 | C2 | semidirect |
| 4. #20241991 | C2 | semidirect |
| 5. #20241897 | C2 | semidirect |
| 6. #20241280 | C2 | semidirect |
| 7. C47×#1555 | C2 | semidirect |
| 187. #1555 | D47 | semidirect |
| 220. C47 | #10089 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20254580 | 2 |
| #20253838 | 2 |
| #20249333 | 2 |
| #20241991 | 2 |
| #20241897 | 2 |
| #20241280 | 2 |
| C47×#1555 | 2 |
| #10089 | 47 |