Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
414 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 414 conjugacy classes of subgroups — too many to draw. Only its 89 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. #20242004 | C2 | semidirect |
| 4. #20241953 | C2 | semidirect |
| 6. #20241270 | C2 | semidirect |
| 7. C47×#1302 | C2 | semidirect |
| 10. #15689532 | C4 | semidirect |
| 11. #15689517 | C4 | semidirect |
| 12. #15689492 | C4 | semidirect |
| 13. #15689483 | C4 | semidirect |
| 198. #1302 | D47 | semidirect |
| 233. C47 | #9431 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20254097 | 2 |
| #20252377 | 2 |
| #20242004 | 2 |
| #20241953 | 2 |
| #20241927 | 2 |
| #20241270 | 2 |
| C47×#1302 | 2 |
| #9431 | 47 |