Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
560 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 560 conjugacy classes of subgroups — too many to draw. Only its 107 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. #20252417 | C2 | semidirect |
| 2. C4×#13093941 | C2 | semidirect |
| 3. #20241986 | C2 | semidirect |
| 4. #20241252 | C2 | semidirect |
| 34. #13093935 | D4 | semidirect |
| 225. C47 | #9187 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20252417 | 2 |
| C4×#13093941 | 2 |
| #20241986 | 2 |
| #20241252 | 2 |
| C47×#2631 | 2 |
| #9187 | 47 |