Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
2122 conjugacy classes of subgroups.
The subgroup lattice has 360 nodes — too large to display as a diagram.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #20252054 | C2 | semidirect |
| 2. #20252026 | C2 | semidirect |
| 3. #20252021 | C2 | semidirect |
| 4. C2×#15689147 | C2 | semidirect |
| 6. #20251807 | C2 | semidirect |
| 9. #15689184 | C22 | semidirect |
| 10. #15689180 | C22 | semidirect |
| 11. #15689176 | C22 | semidirect |
| 14. #15689147 | C22 | semidirect |
| 15. C2×C4⋊(C47⋊C8) | C22 | semidirect |
| 18. #15689079 | C22 | semidirect |
| 210. C47 | #60125 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20252054 | 2 |
| #20252026 | 2 |
| #20252021 | 2 |
| C2×#15689147 | 2 |
| #20251833 | 2 |
| #20251807 | 2 |
| C2×C4×#41×C47 | 2 |
| #60125 | 47 |