Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
372 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 73 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. #20245007 | C2 | semidirect |
| 3. #20243437 | C2 | semidirect |
| 4. #20241382 | C2 | semidirect |
| 5. #20241380 | C2 | semidirect |
| 6. #20241378 | C2 | semidirect |
| 7. C47×#1342 | C2 | semidirect |
| 180. #1342 | D47 | semidirect |
| 208. C47 | #11872 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20253052 | 2 |
| #20245007 | 2 |
| #20243437 | 2 |
| #20241382 | 2 |
| #20241380 | 2 |
| #20241378 | 2 |
| C47×#1342 | 2 |
| #11872 | 47 |