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. #20243275 | C2 | semidirect |
| 6. #20241489 | C2 | semidirect |
| 7. C47×#1389 | C2 | semidirect |
| 11. #15689234 | C4 | semidirect |
| 12. #15689229 | C4 | semidirect |
| 18. #15688934 | C4 | semidirect |
| 19. #15688929 | C4 | semidirect |
| 43. C2×C47⋊C16 | C2×C4 | semidirect |
| 45. #13093956 | C2×C4 | semidirect |
| 56. M32×C47 | C2×C4 | semidirect |
| 59. #108×C47 | C2×C4 | semidirect |
| 152. #1389 | D47 | semidirect |
| 176. C47 | #12649 | semidirect |
| 199. M32 | C4×D47 | semidirect |
| 203. #108 | C4×D47 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20252188 | 2 |
| #20245125 | 2 |
| #20245115 | 2 |
| C2×#15688900 | 2 |
| #20243275 | 2 |
| #20241489 | 2 |
| C47×#1389 | 2 |
| #12649 | 47 |