Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
1882 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. Q8×#10625329 | C2 | semidirect |
| 2. #20252337 | C2 | semidirect |
| 3. #20252323 | C2 | semidirect |
| 4. C2×Q8×C47⋊C8 | C2 | semidirect |
| 32. #13094031 | Q8 | direct (N × H) |
| 88. #10625329 | C2×Q8 | semidirect |
| 90. C2×C47⋊C8 | C2×Q8 | semidirect |
| 99. Q8×C47 | #131 | semidirect |
| 161. C47 | Q8×#131 | semidirect |
| 230. Q8 | #13094031 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×#10625329 | 2 |
| #20252337 | 2 |
| #20252323 | 2 |
| C2×Q8×C47⋊C8 | 2 |
| #20251956 | 2 |
| C4×#13094031 | 2 |
| Q8×#41×C47 | 2 |
| Q8×#131 | 47 |