Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
1974 conjugacy classes of subgroups.
The subgroup lattice has 314 nodes — too large to display as a diagram.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #20252477 | C2 | semidirect |
| 2. #20252473 | C2 | semidirect |
| 3. #20252469 | C2 | semidirect |
| 4. Q8×#10625329 | C2 | semidirect |
| 7. #15689254 | C22 | semidirect |
| 8. Q8×C47⋊C8 | C22 | semidirect |
| 67. C2×Q8×C47 | M16 | semidirect |
| 183. C47 | #60248 | semidirect |
| 224. C2×Q8 | #10625329 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20252477 | 2 |
| #20252473 | 2 |
| #20252469 | 2 |
| Q8×#10625329 | 2 |
| #20252021 | 2 |
| C22×C4×Q8×C47 | 2 |
| #60248 | 47 |