Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
500 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 77 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. #20243851 | C2 | semidirect |
| 3. #20243571 | C2 | semidirect |
| 4. #20241905 | C2 | semidirect |
| 5. #20241904 | C2 | semidirect |
| 6. #20241264 | C2 | semidirect |
| 7. C47×#1900 | C2 | semidirect |
| 226. #1900 | D47 | semidirect |
| 263. C47 | #10557 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20254136 | 2 |
| #20243851 | 2 |
| #20243571 | 2 |
| #20241905 | 2 |
| #20241904 | 2 |
| #20241264 | 2 |
| C47×#1900 | 2 |
| #10557 | 47 |