Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
542 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 542 conjugacy classes of subgroups — too many to draw. Only its 107 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. #20251765 | C2 | semidirect |
| 5. #20242074 | C2 | semidirect |
| 6. #20241220 | C2 | semidirect |
| 7. C47×#1549 | C2 | semidirect |
| 172. #1549 | D47 | semidirect |
| 200. C47 | #10285 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20254518 | 2 |
| #20254516 | 2 |
| #20251765 | 2 |
| #20244215 | 2 |
| #20242074 | 2 |
| #20241220 | 2 |
| C47×#1549 | 2 |
| #10285 | 47 |