Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
392 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 79 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 |
|---|---|---|
| 3. #20242086 | C2 | semidirect |
| 4. #20241888 | C2 | semidirect |
| 6. #20241245 | C2 | semidirect |
| 7. C47×#1573 | C2 | semidirect |
| 180. #1573 | D47 | semidirect |
| 212. C47 | #10510 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20254393 | 2 |
| #20244318 | 2 |
| #20242086 | 2 |
| #20241888 | 2 |
| #20241739 | 2 |
| #20241245 | 2 |
| C47×#1573 | 2 |
| #10510 | 47 |