Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
456 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 111 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. #20241399 | C2 | semidirect |
| 5. C22×Dic188 | C4 | semidirect |
| 10. #15689364 | C4 | semidirect |
| 12. C2×#13093958 | C4 | semidirect |
| 167. C47 | #11706 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15689364 | 2 |
| #20244999 | 2 |
| #20241399 | 2 |
| C47×#1735 | 2 |
| #11706 | 47 |