Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
200 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 200 conjugacy classes of subgroups — too many to draw. Only its 65 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. Q32×Dic47 | C2 | semidirect |
| 4. #20241587 | C2 | semidirect |
| 6. #20241521 | C2 | semidirect |
| 7. C47×#1416 | C2 | semidirect |
| 11. #15688960 | C4 | semidirect |
| 30. C47⋊C32 | C2×C4 | semidirect |
| 33. Q32×C47 | C2×C4 | semidirect |
| 86. #1416 | D47 | semidirect |
| 105. C47 | #13652 | semidirect |
| 111. Q32 | C4×D47 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15688960 | 2 |
| Q32×Dic47 | 2 |
| #20245234 | 2 |
| #20241587 | 2 |
| #20241567 | 2 |
| #20241521 | 2 |
| C47×#1416 | 2 |
| #13652 | 47 |