Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
420 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 420 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 |
|---|---|---|
| 1. #20245154 | C2 | semidirect |
| 2. #20245016 | C2 | semidirect |
| 3. C2×#15688905 | C2 | semidirect |
| 4. #20244993 | C2 | semidirect |
| 24. #13093964 | D4 | semidirect |
| 159. C47 | #13201 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20245154 | 2 |
| #20245016 | 2 |
| C2×#15688905 | 2 |
| #20244993 | 2 |
| C47×#2930 | 2 |
| #13201 | 47 |