Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
732 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 732 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 |
|---|---|---|
| 2. #20244368 | C2 | semidirect |
| 3. #20242108 | C2 | semidirect |
| 4. #20242025 | C2 | semidirect |
| 5. #20241897 | C2 | semidirect |
| 6. #20241896 | C2 | semidirect |
| 7. C47×#1557 | C2 | semidirect |
| 13. #15689778 | C4 | semidirect |
| 14. #15689777 | C4 | semidirect |
| 215. #1557 | D47 | semidirect |
| 250. C47 | #8494 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20257786 | 2 |
| #20244368 | 2 |
| #20242108 | 2 |
| #20242025 | 2 |
| #20241897 | 2 |
| #20241896 | 2 |
| C47×#1557 | 2 |
| #8494 | 47 |