Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
528 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 528 conjugacy classes of subgroups — too many to draw. Only its 131 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 |
|---|---|---|
| 2. C2×#15688932 | C2 | semidirect |
| 3. #20244999 | C2 | semidirect |
| 4. #20241495 | C2 | semidirect |
| 5. C2×C47×#427 | C2 | semidirect |
| 9. #15689364 | C4 | semidirect |
| 10. #15689359 | C4 | semidirect |
| 54. #106×C47 | D4 | semidirect |
| 153. C2×#427 | D47 | semidirect |
| 178. C47 | #13002 | semidirect |
| 210. #106 | C22⋊D47 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20252969 | 2 |
| C2×#15688932 | 2 |
| #20244999 | 2 |
| #20241495 | 2 |
| C2×C47×#427 | 2 |
| #13002 | 47 |