Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
312 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 312 conjugacy classes of subgroups — too many to draw. Only its 101 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. #20244985 | C2 | semidirect |
| 5. #20241502 | C2 | semidirect |
| 6. #20241485 | C2 | semidirect |
| 7. C47×#1953 | C2 | semidirect |
| 14. #15688938 | C4 | semidirect |
| 15. #15688935 | C4 | semidirect |
| 140. #1953 | D47 | semidirect |
| 165. C47 | #13146 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20245135 | 2 |
| C2×#15688929 | 2 |
| #20244985 | 2 |
| #20244286 | 2 |
| #20241502 | 2 |
| #20241485 | 2 |
| C47×#1953 | 2 |
| #13146 | 47 |