Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
472 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 99 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. #20252408 | C2 | semidirect |
| 3. #20241979 | C2 | semidirect |
| 4. #20241895 | C2 | semidirect |
| 5. #20241281 | C2 | semidirect |
| 6. #20241260 | C2 | semidirect |
| 7. C47×#1759 | C2 | semidirect |
| 10. #15689408 | C4 | semidirect |
| 11. #15689403 | C4 | semidirect |
| 12. #15689323 | C4 | semidirect |
| 13. #15689318 | C4 | semidirect |
| 199. #1759 | D47 | semidirect |
| 235. C47 | #9162 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20253539 | 2 |
| #20252408 | 2 |
| #20241979 | 2 |
| #20241895 | 2 |
| #20241281 | 2 |
| #20241260 | 2 |
| C47×#1759 | 2 |
| #9162 | 47 |