Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
412 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 97 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 |
|---|---|---|
| 3. #20242179 | C2 | semidirect |
| 5. #20241220 | C2 | semidirect |
| 6. #20241220 | C2 | semidirect |
| 7. C47×#1574 | C2 | semidirect |
| 20. #15688871 | C4 | semidirect |
| 21. #15688871 | C4 | semidirect |
| 22. #15688866 | C4 | semidirect |
| 23. #15688866 | C4 | semidirect |
| 161. #1574 | D47 | semidirect |
| 191. C47 | #8935 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20252454 | 2 |
| #20244215 | 2 |
| #20242179 | 2 |
| #20242048 | 2 |
| #20241220 | 2 |
| C47×#1574 | 2 |
| #8935 | 47 |