Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
474 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 474 conjugacy classes of subgroups — too many to draw. Only its 91 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. #20252400 | C2 | semidirect |
| 3. #20243201 | C2 | semidirect |
| 4. #20241979 | C2 | semidirect |
| 5. #20241897 | C2 | semidirect |
| 6. #20241280 | C2 | semidirect |
| 7. C47×#1291 | C2 | semidirect |
| 11. #15689409 | C4 | semidirect |
| 12. #15689404 | C4 | semidirect |
| 13. #15689324 | C4 | semidirect |
| 14. #15689319 | C4 | semidirect |
| 203. #1291 | D47 | semidirect |
| 235. C47 | #9161 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20253540 | 2 |
| #20252400 | 2 |
| #20243201 | 2 |
| #20241979 | 2 |
| #20241897 | 2 |
| #20241280 | 2 |
| C47×#1291 | 2 |
| #9161 | 47 |