Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
566 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 566 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 |
|---|---|---|
| 2. #20248555 | C2 | semidirect |
| 3. #20244308 | C2 | semidirect |
| 4. #20241990 | C2 | semidirect |
| 5. #20241830 | C2 | semidirect |
| 6. #20241245 | C2 | semidirect |
| 7. C47×#3234 | C2 | semidirect |
| 210. #3234 | D47 | semidirect |
| 249. C47 | #10005 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20253475 | 2 |
| #20248555 | 2 |
| #20244308 | 2 |
| #20241990 | 2 |
| #20241830 | 2 |
| #20241245 | 2 |
| C47×#3234 | 2 |
| #10005 | 47 |