Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
428 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 428 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. #20243274 | C2 | semidirect |
| 6. #20241504 | C2 | semidirect |
| 7. C47×#1384 | C2 | semidirect |
| 11. #15689234 | C4 | semidirect |
| 12. #15689229 | C4 | semidirect |
| 18. #15688932 | C4 | semidirect |
| 19. #15688931 | C4 | semidirect |
| 42. #13093964 | C2×C4 | semidirect |
| 45. #13093960 | C2×C4 | semidirect |
| 57. C2×C16×C47 | C2×C4 | semidirect |
| 61. #106×C47 | C2×C4 | semidirect |
| 153. #1384 | D47 | semidirect |
| 176. C47 | #12649 | semidirect |
| 201. C2×C16 | C4×D47 | semidirect |
| 207. #106 | C4×D47 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20252188 | 2 |
| #20245123 | 2 |
| #20245117 | 2 |
| C2×#15688900 | 2 |
| #20243274 | 2 |
| #20241504 | 2 |
| C47×#1384 | 2 |
| #12649 | 47 |