Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
498 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 498 conjugacy classes of subgroups — too many to draw. Only its 79 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 |
|---|---|---|
| 1. #20245053 | C2 | semidirect |
| 2. #20241980 | C2 | semidirect |
| 3. #20241539 | C2 | semidirect |
| 7. #15688918 | C22 | semidirect |
| 10. #15688863 | C22 | semidirect |
| 11. C47×#585 | C4 | semidirect |
| 14. C47×#456 | C4 | semidirect |
| 19. C47×#413 | C4 | semidirect |
| 179. #585 | Dic47 | semidirect |
| 182. #456 | Dic47 | semidirect |
| 187. #413 | Dic47 | semidirect |
| 194. C47 | #13568 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20245053 | 2 |
| #20241980 | 2 |
| #20241539 | 2 |
| C47×#3018 | 2 |
| #13568 | 47 |