Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
508 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 508 conjugacy classes of subgroups — too many to draw. Only its 95 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. #20252422 | C2 | semidirect |
| 3. #20243216 | C2 | semidirect |
| 4. #20241999 | C2 | semidirect |
| 5. #20241288 | C2 | semidirect |
| 6. #20241244 | C2 | semidirect |
| 7. C47×#1502 | C2 | semidirect |
| 10. #15689410 | C4 | semidirect |
| 11. #15689410 | C4 | semidirect |
| 12. #15689315 | C4 | semidirect |
| 13. #15689315 | C4 | semidirect |
| 217. #1502 | D47 | semidirect |
| 253. C47 | #9163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20253475 | 2 |
| #20252422 | 2 |
| #20243216 | 2 |
| #20241999 | 2 |
| #20241288 | 2 |
| #20241244 | 2 |
| C47×#1502 | 2 |
| #9163 | 47 |