Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
468 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 468 conjugacy classes of subgroups — too many to draw. Only its 87 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. #20245060 | C2 | semidirect |
| 3. #20245059 | C2 | semidirect |
| 4. #20245039 | C2 | semidirect |
| 5. #20243432 | C2 | semidirect |
| 6. #20243191 | C2 | semidirect |
| 7. C47×#2122 | C2 | semidirect |
| 8. C22×#10625334 | C4 | semidirect |
| 16. #15689159 | C4 | semidirect |
| 17. #15689128 | C4 | semidirect |
| 18. #15689127 | C4 | semidirect |
| 217. #2122 | D47 | semidirect |
| 250. C47 | #13231 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20253033 | 2 |
| #20245060 | 2 |
| #20245059 | 2 |
| #20245039 | 2 |
| #20243432 | 2 |
| #20243191 | 2 |
| C47×#2122 | 2 |
| #13231 | 47 |