Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
200 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 200 conjugacy classes of subgroups — too many to draw. Only its 61 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×#15688960 | C2 | semidirect |
| 2. C2×#15688957 | C2 | semidirect |
| 4. #20241587 | C2 | semidirect |
| 5. #20241569 | C2 | semidirect |
| 6. #20241565 | C2 | semidirect |
| 7. C47×#2216 | C2 | semidirect |
| 28. C47⋊C32 | D4 | semidirect |
| 93. #2216 | D47 | semidirect |
| 116. C47 | #13699 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15688960 | 2 |
| C2×#15688957 | 2 |
| #20245474 | 2 |
| #20241587 | 2 |
| #20241569 | 2 |
| #20241565 | 2 |
| C47×#2216 | 2 |
| #13699 | 47 |