Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
5206 conjugacy classes of subgroups.
The subgroup lattice has 388 nodes — too large to display as a diagram.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×#13094031 | C2 | semidirect |
| 2. #20251837 | C2 | direct (N × H) |
| 3. C2×#15689090 | C2 | semidirect |
| 4. C2×#15689087 | C2 | semidirect |
| 5. C22×C22⋊(C47⋊C8) | C2 | semidirect |
| 8. C2×#13094031 | C22 | semidirect |
| 9. C22×#10625329 | C22 | semidirect |
| 10. C23×C47⋊C8 | C22 | semidirect |
| 11. #15689090 | C22 | semidirect |
| 12. #15689087 | C22 | semidirect |
| 15. C2×C22⋊(C47⋊C8) | C22 | semidirect |
| 16. C2×C22⋊(C47⋊C8) | C22 | semidirect |
| 17. C2×C22⋊(C47⋊C8) | C22 | semidirect |
| 30. C2×#10625329 | C23 | semidirect |
| 34. C22×C47⋊C8 | C23 | semidirect |
| 37. C22⋊(C47⋊C8) | C23 | semidirect |
| 38. C22⋊(C47⋊C8) | C23 | semidirect |
| 134. C23×C47 | #131 | semidirect |
| 179. C22×C47 | C2×#131 | semidirect |
| 196. C2×C47 | #2880 | semidirect |
| 221. C47 | C2×#2880 | semidirect |
| 328. C23 | #13094031 | semidirect |
| 372. C22 | C2×#13094031 | semidirect |
| 383. C2 | #20251837 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13094031 | 2 |
| #20251837 | 2 |
| C2×#15689090 | 2 |
| C2×#15689087 | 2 |
| C22×C22⋊(C47⋊C8) | 2 |
| C23×#41×C47 | 2 |
| C2×#2880 | 47 |