Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
338 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 67 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. #20245613 | C2 | semidirect |
| 3. #20242789 | C2 | semidirect |
| 4. #20241435 | C2 | semidirect |
| 5. #20241366 | C2 | semidirect |
| 6. #20241349 | C2 | semidirect |
| 7. C47×#2226 | C2 | semidirect |
| 133. #2226 | D47 | semidirect |
| 160. C47 | #12384 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20256362 | 2 |
| #20245613 | 2 |
| #20242789 | 2 |
| #20241435 | 2 |
| #20241366 | 2 |
| #20241349 | 2 |
| C47×#2226 | 2 |
| #12384 | 47 |