Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
378 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 378 conjugacy classes of subgroups — too many to draw. Only its 115 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. #20243516 | C2 | semidirect |
| 3. #20241398 | C2 | semidirect |
| 4. C47×#2162 | C2 | semidirect |
| 6. #15689528 | C4 | semidirect |
| 7. #15689500 | C4 | semidirect |
| 12. C4×D376 | C4 | semidirect |
| 126. #2162 | D47 | semidirect |
| 150. C47 | #11856 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20253967 | 2 |
| #20243516 | 2 |
| #20241398 | 2 |
| C47×#2162 | 2 |
| #11856 | 47 |