Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
914 conjugacy classes of subgroups; only the 159 normal subgroups are shown.
This group has 914 conjugacy classes of subgroups — too many to draw. Only its 159 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. #20245137 | C2 | semidirect |
| 2. #20245116 | C2 | semidirect |
| 3. C2×#15688905 | C2 | semidirect |
| 4. #20243430 | C2 | semidirect |
| 6. C2×#13093964 | C22 | semidirect |
| 7. C2×#13093960 | C22 | semidirect |
| 8. C2×#13093960 | C22 | semidirect |
| 216. C47 | #12740 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20245137 | 2 |
| #20245116 | 2 |
| C2×#15688905 | 2 |
| #20243430 | 2 |
| C2×C47×#575 | 2 |
| #12740 | 47 |