Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
688 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 688 conjugacy classes of subgroups — too many to draw. Only its 99 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #20251849 | C2 | semidirect |
| 3. #20245059 | C2 | semidirect |
| 4. #20245039 | C2 | semidirect |
| 5. #20241518 | C2 | semidirect |
| 6. #20241508 | C2 | semidirect |
| 7. C47×#1795 | C2 | semidirect |
| 8. C2×#13094049 | C4 | semidirect |
| 9. C22×#10625334 | C4 | semidirect |
| 16. #15689128 | C4 | semidirect |
| 17. #15689119 | C4 | semidirect |
| 31. C22×D188 | C2×C4 | semidirect |
| 38. C2×#10625329 | C2×C4 | semidirect |
| 39. C22×C47⋊C8 | C2×C4 | semidirect |
| 50. #13093983 | C2×C4 | semidirect |
| 254. #1795 | D47 | semidirect |
| 289. C47 | #13102 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20252656 | 2 |
| #20251849 | 2 |
| #20245059 | 2 |
| #20245039 | 2 |
| #20241518 | 2 |
| #20241508 | 2 |
| C47×#1795 | 2 |
| #13102 | 47 |