Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
412 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 123 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 |
|---|---|---|
| 4. C2×#15688900 | C2 | semidirect |
| 5. #20243296 | C2 | semidirect |
| 6. #20241491 | C2 | semidirect |
| 7. C47×#1388 | C2 | semidirect |
| 17. #15688940 | C4 | semidirect |
| 18. #15688937 | C4 | semidirect |
| 19. #15688929 | C4 | semidirect |
| 145. #1388 | D47 | semidirect |
| 169. C47 | #12651 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15689244 | 2 |
| #20245138 | 2 |
| #20245115 | 2 |
| C2×#15688900 | 2 |
| #20243296 | 2 |
| #20241491 | 2 |
| C47×#1388 | 2 |
| #12651 | 47 |