Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
200 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 200 conjugacy classes of subgroups — too many to draw. Only its 57 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×#15688956 | C2 | semidirect |
| 2. #20245476 | C2 | semidirect |
| 4. #20241588 | C2 | semidirect |
| 5. #20241569 | C2 | semidirect |
| 6. #20241566 | C2 | semidirect |
| 7. C2×C47×SD64 | C2 | semidirect |
| 39. C32×C47 | D4 | semidirect |
| 91. C2×SD64 | D47 | semidirect |
| 116. C47 | #13699 | semidirect |
| 135. C32 | C22⋊D47 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15688956 | 2 |
| #20245476 | 2 |
| #20245471 | 2 |
| #20241588 | 2 |
| #20241569 | 2 |
| #20241566 | 2 |
| C2×C47×SD64 | 2 |
| #13699 | 47 |