Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
452 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 452 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 |
|---|---|---|
| 2. #20252560 | C2 | semidirect |
| 3. #20244221 | C2 | semidirect |
| 4. #20241875 | C2 | semidirect |
| 5. #20241280 | C2 | semidirect |
| 6. #20241279 | C2 | semidirect |
| 7. C47×#1496 | C2 | semidirect |
| 9. #15689529 | C4 | semidirect |
| 10. #15689510 | C4 | semidirect |
| 11. #15689487 | C4 | semidirect |
| 12. #15689485 | C4 | semidirect |
| 214. #1496 | D47 | semidirect |
| 250. C47 | #8997 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20253977 | 2 |
| #20252560 | 2 |
| #20244221 | 2 |
| #20241875 | 2 |
| #20241280 | 2 |
| #20241279 | 2 |
| C47×#1496 | 2 |
| #8997 | 47 |