Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
286 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 286 conjugacy classes of subgroups — too many to draw. Only its 65 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. #20245671 | C2 | semidirect |
| 3. #20242903 | C2 | semidirect |
| 4. #20241439 | C2 | semidirect |
| 5. #20241369 | C2 | semidirect |
| 68. D8×C47 | Q16 | semidirect |
| 162. C47 | #12414 | semidirect |
| 205. D8 | #10625337 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20256344 | 2 |
| #20245671 | 2 |
| #20242903 | 2 |
| #20241439 | 2 |
| #20241369 | 2 |
| #20241355 | 2 |
| C47×#2226 | 2 |
| #12414 | 47 |