Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
324 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 95 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. #20243519 | C2 | semidirect |
| 3. #20241401 | C2 | semidirect |
| 5. C47×#2162 | C2 | semidirect |
| 7. #15689525 | C4 | semidirect |
| 8. #15689507 | C4 | semidirect |
| 13. C4×Dic188 | C4 | semidirect |
| 15. C4×D376 | C4 | semidirect |
| 138. #2162 | D47 | semidirect |
| 164. C47 | #11855 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20253958 | 2 |
| #20243519 | 2 |
| #20241401 | 2 |
| #20241398 | 2 |
| C47×#2162 | 2 |
| #11855 | 47 |