Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
2110 conjugacy classes of subgroups.
The subgroup lattice has 492 nodes — too large to display as a diagram.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #20243114 | C2 | direct (N × H) |
| 4. C2×#15688887 | C2 | semidirect |
| 20. #15688887 | C22 | semidirect |
| 248. C2×C47 | #1738 | semidirect |
| 274. C47 | C2×#1738 | semidirect |
| 488. C2 | #20243114 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#10625329 | 2 |
| #20243114 | 2 |
| C2×#15688887 | 2 |
| C23×M16×C47 | 2 |
| C2×#1738 | 47 |