Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
582 conjugacy classes of subgroups; only the 159 normal subgroups are shown.
This group has 582 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 |
|---|---|---|
| 3. #20245635 | C2 | semidirect |
| 4. #20245634 | C2 | semidirect |
| 5. #20245633 | C2 | semidirect |
| 6. #20245632 | C2 | semidirect |
| 9. C47×#2245 | C2 | semidirect |
| 149. #2245 | D47 | direct (N × H) |
| 154. D47 | #2245 | direct (N × H) |
| 180. C47 | C2×#2245 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #499×D47 | 2 |
| #494×D47 | 2 |
| #20245635 | 2 |
| #20245634 | 2 |
| #20245633 | 2 |
| #20245632 | 2 |
| #358×D47 | 2 |
| #346×D47 | 2 |
| C47×#2245 | 2 |
| C2×#2245 | 47 |