Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
376 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 376 conjugacy classes of subgroups — too many to draw. Only its 73 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. #20245007 | C2 | semidirect |
| 3. #20243433 | C2 | semidirect |
| 4. #20241377 | C2 | semidirect |
| 5. #20241375 | C2 | semidirect |
| 6. #20241373 | C2 | semidirect |
| 7. C47×#1339 | C2 | semidirect |
| 8. C2×#13094043 | C4 | semidirect |
| 12. #15689382 | C4 | semidirect |
| 14. #15689373 | C4 | semidirect |
| 18. #106×D47 | C4 | semidirect |
| 184. #1339 | D47 | semidirect |
| 210. C47 | #11867 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20253048 | 2 |
| #20245007 | 2 |
| #20243433 | 2 |
| #20241377 | 2 |
| #20241375 | 2 |
| #20241373 | 2 |
| C47×#1339 | 2 |
| #11867 | 47 |