Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
256 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 69 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. #20242981 | C2 | semidirect |
| 3. D8×C47⋊C8 | C2 | semidirect |
| 4. #20241451 | C2 | semidirect |
| 5. #20241443 | C2 | semidirect |
| 6. #20241435 | C2 | semidirect |
| 7. C47×#2224 | C2 | semidirect |
| 52. D8×C47 | SD16 | semidirect |
| 96. C47⋊C8 | D16 | semidirect |
| 112. #2224 | D47 | semidirect |
| 139. C47 | #12416 | semidirect |
| 174. D8 | #10625336 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20245423 | 2 |
| #20242981 | 2 |
| D8×C47⋊C8 | 2 |
| #20241451 | 2 |
| #20241443 | 2 |
| #20241435 | 2 |
| C47×#2224 | 2 |
| #12416 | 47 |