Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
652 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 652 conjugacy classes of subgroups — too many to draw. Only its 105 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. #20244366 | C2 | semidirect |
| 4. #20242069 | C2 | semidirect |
| 6. #20241220 | C2 | semidirect |
| 7. C47×#3209 | C2 | semidirect |
| 174. #3209 | D47 | semidirect |
| 207. C47 | #10291 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20254326 | 2 |
| #20251746 | 2 |
| #20244366 | 2 |
| #20242069 | 2 |
| #20242055 | 2 |
| #20241220 | 2 |
| C47×#3209 | 2 |
| #10291 | 47 |