Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
316 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 316 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 |
|---|---|---|
| 22. #13093964 | Q8 | semidirect |
| 120. C47 | #13270 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20245154 | 2 |
| #20244993 | 2 |
| #20241474 | 2 |
| #20241470 | 2 |
| C47×#2960 | 2 |
| #13270 | 47 |