Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
768 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 768 conjugacy classes of subgroups — too many to draw. Only its 85 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. #20254136 | C2 | semidirect |
| 2. #20252640 | C2 | semidirect |
| 3. #20243300 | C2 | semidirect |
| 4. #20241749 | C2 | semidirect |
| 5. #20241748 | C2 | semidirect |
| 6. #20241264 | C2 | semidirect |
| 7. C47×#3006 | C2 | semidirect |
| 249. #3006 | D47 | semidirect |
| 288. C47 | #9974 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20254136 | 2 |
| #20252640 | 2 |
| #20243300 | 2 |
| #20241749 | 2 |
| #20241748 | 2 |
| #20241264 | 2 |
| C47×#3006 | 2 |
| #9974 | 47 |