Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
420 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 93 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 |
|---|---|---|
| 2. #20243404 | C2 | semidirect |
| 5. #20241711 | C2 | semidirect |
| 6. #20241248 | C2 | semidirect |
| 7. C47×#1571 | C2 | semidirect |
| 178. #1571 | D47 | semidirect |
| 208. C47 | #10466 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20252862 | 2 |
| #20243404 | 2 |
| #20242038 | 2 |
| #20241949 | 2 |
| #20241711 | 2 |
| #20241248 | 2 |
| C47×#1571 | 2 |
| #10466 | 47 |