Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
568 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 568 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 |
|---|---|---|
| 1. #20256522 | C2 | semidirect |
| 2. C2×#15689559 | C2 | semidirect |
| 3. #20245124 | C2 | semidirect |
| 4. #20245104 | C2 | semidirect |
| 5. #20244286 | C2 | semidirect |
| 6. #20241474 | C2 | semidirect |
| 7. C47×#3155 | C2 | semidirect |
| 38. C2×Dic188 | D4 | semidirect |
| 40. C2×D376 | D4 | semidirect |
| 51. #13093964 | D4 | semidirect |
| 53. C2×C47⋊C16 | D4 | semidirect |
| 213. #3155 | D47 | semidirect |
| 250. C47 | #13334 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20256522 | 2 |
| C2×#15689559 | 2 |
| #20245124 | 2 |
| #20245104 | 2 |
| #20244286 | 2 |
| #20241474 | 2 |
| C47×#3155 | 2 |
| #13334 | 47 |