Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
456 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 89 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. #20246493 | C2 | semidirect |
| 3. #20242014 | C2 | semidirect |
| 6. #20241282 | C2 | semidirect |
| 7. C47×#1300 | C2 | semidirect |
| 10. #15689492 | C4 | semidirect |
| 11. #15689488 | C4 | semidirect |
| 190. #1300 | D47 | semidirect |
| 220. C47 | #9442 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20253789 | 2 |
| #20246493 | 2 |
| #20242014 | 2 |
| #20241897 | 2 |
| #20241895 | 2 |
| #20241282 | 2 |
| C47×#1300 | 2 |
| #9442 | 47 |