Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
4894 conjugacy classes of subgroups.
The subgroup lattice has 306 nodes — too large to display as a diagram.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. C2×#15689022 | C2 | direct (N × H) |
| 16. #15689022 | C22 | direct (N × H) |
| 20. C22×C4⋊C4×C47 | C4 | semidirect |
| 50. C2×C4⋊C4×C47 | C2×C4 | semidirect |
| 63. C22×C4×C47 | C4⋊C4 | semidirect |
| 85. C4⋊C4×C47 | C22×C4 | semidirect |
| 107. C2×C4×C47 | C2×C4⋊C4 | semidirect |
| 125. C22×C47 | #389 | semidirect |
| 141. C4×C47 | C22×C4⋊C4 | semidirect |
| 151. C2×C47 | C2×#389 | semidirect |
| 168. C22×C4⋊C4 | Dic47 | semidirect |
| 174. C47 | C22×#389 | semidirect |
| 200. C2×C4⋊C4 | C2×Dic47 | semidirect |
| 231. C22×C4 | C4⋊Dic47 | semidirect |
| 240. C4⋊C4 | C22×Dic47 | semidirect |
| 272. C2×C4 | C2×C4⋊Dic47 | semidirect |
| 277. C22 | #15689022 | direct (N × H) |
| 296. C4 | C22×C4⋊Dic47 | semidirect |
| 297. C2 | C2×#15689022 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C4⋊Dic47 | 2 |
| C23×C4×Dic47 | 2 |
| C2×#15689022 | 2 |
| C22×C47⋊#95 | 2 |
| C23×C4⋊C4×C47 | 2 |
| C22×#389 | 47 |