Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
498 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 498 conjugacy classes of subgroups — too many to draw. Only its 71 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. #20245053 | C2 | semidirect |
| 3. #20241540 | C2 | semidirect |
| 4. C47×#1525 | C2 | semidirect |
| 5. #15689959 | C4 | semidirect |
| 7. #15689305 | C4 | semidirect |
| 12. #15689107 | C4 | semidirect |
| 14. #15688918 | C22 | semidirect |
| 19. C47×#329 | C22 | semidirect |
| 171. #1525 | D47 | semidirect |
| 193. #329 | C2×D47 | semidirect |
| 194. C47 | #13568 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20252736 | 2 |
| #20245053 | 2 |
| #20241540 | 2 |
| C47×#1525 | 2 |
| #13568 | 47 |