Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
728 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 728 conjugacy classes of subgroups — too many to draw. Only its 111 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. #20244333 | C2 | semidirect |
| 3. #20244318 | C2 | semidirect |
| 4. #20241987 | C2 | semidirect |
| 5. #20241914 | C2 | semidirect |
| 6. #20241799 | C2 | semidirect |
| 7. C47×#1552 | C2 | semidirect |
| 8. #15689877 | C4 | semidirect |
| 9. #15689871 | C4 | semidirect |
| 271. #1552 | D47 | semidirect |
| 311. C47 | #8511 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20257953 | 2 |
| #20244333 | 2 |
| #20244318 | 2 |
| #20241987 | 2 |
| #20241914 | 2 |
| #20241799 | 2 |
| C47×#1552 | 2 |
| #8511 | 47 |