Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
1128 conjugacy classes of subgroups; only the 351 normal subgroups are shown.
This group has 1128 conjugacy classes of subgroups — too many to draw. Only its 351 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. #20251983 | C2 | semidirect |
| 3. #20245125 | C2 | semidirect |
| 4. C2×#15688934 | C2 | semidirect |
| 5. C47×#3407 | C2 | semidirect |
| 7. #15689940 | C4 | semidirect |
| 9. #15689928 | C4 | semidirect |
| 14. #15689161 | C22 | semidirect |
| 15. C2×#13093956 | C22 | semidirect |
| 16. #15688934 | C22 | semidirect |
| 17. #15688934 | C22 | semidirect |
| 20. C2×M32×C47 | C22 | semidirect |
| 31. #13094046 | C2×C4 | semidirect |
| 33. C2×Dic188 | C2×C4 | semidirect |
| 35. C2×D376 | C2×C4 | semidirect |
| 123. #3407 | D47 | semidirect |
| 140. C2×M32 | C2×D47 | semidirect |
| 146. C47 | #33388 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20258162 | 2 |
| #20251983 | 2 |
| #20245125 | 2 |
| C2×#15688934 | 2 |
| C47×#3407 | 2 |
| #33388 | 47 |