Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
324 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 99 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. C2×#15688952 | C2 | semidirect |
| 4. #20243270 | C2 | semidirect |
| 5. #20241484 | C2 | semidirect |
| 6. #20241465 | C2 | semidirect |
| 16. #15688927 | C4 | semidirect |
| 17. #15688927 | C4 | semidirect |
| 18. #15688924 | C4 | semidirect |
| 19. #15688924 | C4 | semidirect |
| 178. C47 | #13134 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15688952 | 2 |
| #20245095 | 2 |
| #20244277 | 2 |
| #20243270 | 2 |
| #20241484 | 2 |
| #20241465 | 2 |
| C2×C47×#359 | 2 |
| #13134 | 47 |