Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
2190 conjugacy classes of subgroups.
The subgroup lattice has 540 nodes — too large to display as a diagram.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #20243126 | C2 | direct (N × H) |
| 4. C2×#15688891 | C2 | semidirect |
| 9. C22×#10625329 | C4 | semidirect |
| 24. #15688891 | C22 | semidirect |
| 29. C22×M16×C47 | C4 | semidirect |
| 41. C2×#10625329 | C2×C4 | semidirect |
| 90. C2×M16×C47 | C2×C4 | semidirect |
| 272. C2×C47 | #1742 | semidirect |
| 285. C22×M16 | Dic47 | semidirect |
| 302. C47 | C2×#1742 | semidirect |
| 335. C2×M16 | C2×Dic47 | semidirect |
| 536. C2 | #20243126 | 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 |
| C22×#13093983 | 2 |
| #20243126 | 2 |
| C2×#15688891 | 2 |
| C23×M16×C47 | 2 |
| C2×#1742 | 47 |