Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
484 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 109 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. #135×Dic47 | C2 | semidirect |
| 3. #20245125 | C2 | semidirect |
| 4. #20244274 | C2 | semidirect |
| 5. #20241502 | C2 | semidirect |
| 6. #20241469 | C2 | semidirect |
| 7. C47×#2143 | C2 | semidirect |
| 11. #15689563 | C4 | semidirect |
| 13. #15689558 | C4 | semidirect |
| 34. C2×Dic188 | C2×C4 | semidirect |
| 36. C2×D376 | C2×C4 | semidirect |
| 50. #13093964 | C2×C4 | semidirect |
| 189. #2143 | D47 | semidirect |
| 220. C47 | #13027 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20256522 | 2 |
| #135×Dic47 | 2 |
| #20245125 | 2 |
| #20244274 | 2 |
| #20241502 | 2 |
| #20241469 | 2 |
| C47×#2143 | 2 |
| #13027 | 47 |