Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
334 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 334 conjugacy classes of subgroups — too many to draw. Only its 89 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. #20243507 | C2 | semidirect |
| 3. #20242160 | C2 | semidirect |
| 6. #20241216 | C2 | semidirect |
| 7. C47×#1571 | C2 | semidirect |
| 126. #1571 | D47 | semidirect |
| 149. C47 | #10665 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20244219 | 2 |
| #20243507 | 2 |
| #20242160 | 2 |
| #20241788 | 2 |
| #20241786 | 2 |
| #20241216 | 2 |
| C47×#1571 | 2 |
| #10665 | 47 |