Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
298 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 298 conjugacy classes of subgroups — too many to draw. Only its 63 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. #20245633 | C2 | semidirect |
| 3. #20245430 | C2 | semidirect |
| 4. #20241441 | C2 | semidirect |
| 5. #20241354 | C2 | semidirect |
| 6. #20241346 | C2 | semidirect |
| 7. C47×#1689 | C2 | semidirect |
| 144. #1689 | D47 | semidirect |
| 172. C47 | #12350 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20255993 | 2 |
| #20245633 | 2 |
| #20245430 | 2 |
| #20241441 | 2 |
| #20241354 | 2 |
| #20241346 | 2 |
| C47×#1689 | 2 |
| #12350 | 47 |