Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
566 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 566 conjugacy classes of subgroups — too many to draw. Only its 113 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 |
|---|---|---|
| 3. #20241951 | C2 | semidirect |
| 4. #20241888 | C2 | semidirect |
| 6. #20241289 | C2 | semidirect |
| 7. C47×#1286 | C2 | semidirect |
| 12. #15689414 | C4 | semidirect |
| 13. #15689404 | C4 | semidirect |
| 32. #13094024 | C2×C4 | semidirect |
| 33. #13094024 | C2×C4 | semidirect |
| 67. C4⋊C8×C47 | C2×C4 | semidirect |
| 196. #1286 | D47 | semidirect |
| 224. C47 | #9175 | semidirect |
| 256. C4⋊C8 | C4×D47 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20253187 | 2 |
| #20246296 | 2 |
| #20241951 | 2 |
| #20241888 | 2 |
| #20241778 | 2 |
| #20241289 | 2 |
| C47×#1286 | 2 |
| #9175 | 47 |