Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
440 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 440 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 |
|---|---|---|
| 2. #20243241 | C2 | semidirect |
| 3. #20241213 | C2 | semidirect |
| 5. C47×#1831 | C2 | semidirect |
| 169. #1831 | D47 | semidirect |
| 198. C47 | #7696 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20251760 | 2 |
| #20243241 | 2 |
| #20241213 | 2 |
| #20241208 | 2 |
| C47×#1831 | 2 |
| #7696 | 47 |