Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
466 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 466 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 |
|---|---|---|
| 1. C2×#15688936 | C2 | semidirect |
| 2. #20245124 | C2 | semidirect |
| 3. #20245116 | C2 | semidirect |
| 4. #20245104 | C2 | semidirect |
| 5. #20244993 | C2 | semidirect |
| 6. #20243512 | C2 | semidirect |
| 24. C47×#495 | C4 | semidirect |
| 25. C47×#493 | C4 | semidirect |
| 32. #13093964 | D4 | semidirect |
| 34. C2×C47⋊C16 | D4 | semidirect |
| 189. #495 | Dic47 | semidirect |
| 190. #493 | Dic47 | semidirect |
| 201. C47 | #13215 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15688936 | 2 |
| #20245124 | 2 |
| #20245116 | 2 |
| #20245104 | 2 |
| #20244993 | 2 |
| #20243512 | 2 |
| C47×#3155 | 2 |
| #13215 | 47 |