Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
5758 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×C4⋊C4×Dic47 | C2 | direct (N × H) |
| 10. C22×C4⋊Dic47 | C4 | semidirect |
| 13. C22×C4×Dic47 | C4 | semidirect |
| 16. C4⋊C4×Dic47 | C22 | direct (N × H) |
| 20. C22×C4⋊C4×C47 | C4 | semidirect |
| 34. C2×C4⋊Dic47 | C2×C4 | semidirect |
| 37. C2×C4×Dic47 | C2×C4 | semidirect |
| 50. C2×C4⋊C4×C47 | C2×C4 | semidirect |
| 63. C22×C4×C47 | C42 | semidirect |
| 76. C22×Dic47 | C4⋊C4 | direct (N × H) |
| 85. C4⋊C4×C47 | C22×C4 | semidirect |
| 86. C4⋊Dic47 | C22×C4 | semidirect |
| 88. C4×Dic47 | C22×C4 | semidirect |
| 107. C2×C4×C47 | C2×C42 | semidirect |
| 118. C2×Dic47 | C2×C4⋊C4 | direct (N × H) |
| 125. C22×C47 | C4×C4⋊C4 | semidirect |
| 141. C4×C47 | C22×C42 | semidirect |
| 144. Dic47 | C22×C4⋊C4 | direct (N × H) |
| 151. C2×C47 | C2×C4×C4⋊C4 | semidirect |
| 166. C22×C4⋊C4 | Dic47 | direct (N × H) |
| 174. C47 | C22×C4×C4⋊C4 | semidirect |
| 198. C2×C4⋊C4 | C2×Dic47 | direct (N × H) |
| 231. C22×C4 | C4×Dic47 | semidirect |
| 239. C4⋊C4 | C22×Dic47 | direct (N × H) |
| 272. C2×C4 | C2×C4×Dic47 | semidirect |
| 277. C22 | C4⋊C4×Dic47 | direct (N × H) |
| 296. C4 | C22×C4×Dic47 | semidirect |
| 297. C2 | C2×C4⋊C4×Dic47 | 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×C4⋊C4×Dic47 | 2 |
| C22×C47⋊#95 | 2 |
| C23×C4⋊C4×C47 | 2 |
| C22×C4×C4⋊C4 | 47 |