Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
464 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 464 conjugacy classes of subgroups — too many to draw. Only its 85 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. #20252448 | C2 | semidirect |
| 3. #20241942 | C2 | semidirect |
| 4. #20241916 | C2 | semidirect |
| 5. #20241749 | C2 | semidirect |
| 6. #20241264 | C2 | semidirect |
| 7. C47×#1306 | C2 | semidirect |
| 10. #15689454 | C4 | semidirect |
| 12. #15689437 | C4 | semidirect |
| 15. #15689276 | C4 | semidirect |
| 17. #15689259 | C4 | semidirect |
| 223. #1306 | D47 | semidirect |
| 260. C47 | #9332 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20254204 | 2 |
| #20252448 | 2 |
| #20241942 | 2 |
| #20241916 | 2 |
| #20241749 | 2 |
| #20241264 | 2 |
| C47×#1306 | 2 |
| #9332 | 47 |