Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
486 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 486 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 |
|---|---|---|
| 4. #20241887 | C2 | semidirect |
| 5. #20241287 | C2 | semidirect |
| 6. #20241243 | C2 | semidirect |
| 7. C47×#1531 | C2 | semidirect |
| 10. #15689400 | C4 | semidirect |
| 11. #15689400 | C4 | semidirect |
| 12. #15689325 | C4 | semidirect |
| 13. #15689325 | C4 | semidirect |
| 207. #1531 | D47 | semidirect |
| 243. C47 | #9165 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20253483 | 2 |
| #20252425 | 2 |
| #20243214 | 2 |
| #20241887 | 2 |
| #20241287 | 2 |
| #20241243 | 2 |
| C47×#1531 | 2 |
| #9165 | 47 |