Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
542 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 542 conjugacy classes of subgroups — too many to draw. Only its 85 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 |
|---|---|---|
| 4. #20241990 | C2 | semidirect |
| 5. #20241900 | C2 | semidirect |
| 6. #20241280 | C2 | semidirect |
| 7. C47×#3236 | C2 | semidirect |
| 174. #3236 | D47 | semidirect |
| 209. C47 | #10097 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20253764 | 2 |
| #20249334 | 2 |
| #20242101 | 2 |
| #20241990 | 2 |
| #20241900 | 2 |
| #20241280 | 2 |
| C47×#3236 | 2 |
| #10097 | 47 |