Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
712 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 712 conjugacy classes of subgroups — too many to draw. Only its 171 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×#15689564 | C2 | semidirect |
| 3. #20252256 | C2 | semidirect |
| 4. #20245448 | C2 | semidirect |
| 5. #20245426 | C2 | semidirect |
| 6. #20245146 | C2 | semidirect |
| 7. #20245104 | C2 | semidirect |
| 8. #20245096 | C2 | semidirect |
| 9. C22×SD32×C47 | C2 | semidirect |
| 15. C2×#13093970 | C22 | semidirect |
| 16. C2×#13093967 | C22 | semidirect |
| 22. Q16×Dic47 | C22 | semidirect |
| 26. Dic47⋊C16 | C22 | semidirect |
| 27. #15688928 | C22 | semidirect |
| 28. #15688925 | C22 | semidirect |
| 67. C2×Q16×C47 | D4 | semidirect |
| 173. C22×SD32 | D47 | semidirect |
| 211. C47 | #33587 | semidirect |
| 221. C2×Q16 | C22⋊D47 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15689564 | 2 |
| #20253869 | 2 |
| #20252256 | 2 |
| #20245448 | 2 |
| #20245426 | 2 |
| #20245146 | 2 |
| #20245104 | 2 |
| #20245096 | 2 |
| C22×SD32×C47 | 2 |
| #33587 | 47 |