Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
3086 conjugacy classes of subgroups.
The subgroup lattice has 262 nodes — too large to display as a diagram.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#15689176 | C2 | direct (N × H) |
| 2. C22×C4⋊(C47⋊C8) | C2 | semidirect |
| 4. C22×C4×C47⋊C8 | C2 | semidirect |
| 7. #15689176 | C22 | direct (N × H) |
| 8. C2×C4⋊(C47⋊C8) | C22 | semidirect |
| 10. C2×C4×C47⋊C8 | C22 | semidirect |
| 22. C4⋊(C47⋊C8) | C23 | semidirect |
| 24. C4×C47⋊C8 | C23 | semidirect |
| 28. C23×C4×C47 | C8 | semidirect |
| 59. C22×C4×C47 | C2×C8 | semidirect |
| 98. C2×C4×C47 | C22×C8 | semidirect |
| 113. C22×C47 | #431 | semidirect |
| 132. C2×C47 | C2×#431 | semidirect |
| 150. C47 | C22×#431 | semidirect |
| 154. C23×C4 | C47⋊C8 | semidirect |
| 190. C22×C4 | C2×C47⋊C8 | semidirect |
| 229. C2×C4 | C22×C47⋊C8 | semidirect |
| 243. C22 | #15689176 | direct (N × H) |
| 257. C2 | C2×#15689176 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15689176 | 2 |
| C22×C4⋊(C47⋊C8) | 2 |
| C22×C22⋊(C47⋊C8) | 2 |
| C22×C4×C47⋊C8 | 2 |
| C23×C42×C47 | 2 |
| C22×#431 | 47 |