Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
588 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 588 conjugacy classes of subgroups — too many to draw. Only its 111 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. #20245849 | C2 | semidirect |
| 3. #20244215 | C2 | semidirect |
| 4. #20241882 | C2 | semidirect |
| 5. #20241812 | C2 | semidirect |
| 6. #20241220 | C2 | semidirect |
| 7. C47×#1303 | C2 | semidirect |
| 12. #15689404 | C4 | semidirect |
| 13. #15689319 | C4 | semidirect |
| 128. C4×Dic47 | D8 | semidirect |
| 215. #1303 | D47 | semidirect |
| 245. C47 | #9237 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20253389 | 2 |
| #20245849 | 2 |
| #20244215 | 2 |
| #20241882 | 2 |
| #20241812 | 2 |
| #20241220 | 2 |
| C47×#1303 | 2 |
| #9237 | 47 |