Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
422 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 422 conjugacy classes of subgroups — too many to draw. Only its 103 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. C2×C22⋊(C47⋊C16) | C2 | semidirect |
| 3. #20241399 | C2 | semidirect |
| 4. #20241396 | C2 | semidirect |
| 5. C47×#1807 | C2 | semidirect |
| 6. C2×#13094046 | C4 | semidirect |
| 9. #15689364 | C4 | semidirect |
| 11. #15689359 | C4 | semidirect |
| 15. #15689161 | C4 | semidirect |
| 167. #1807 | D47 | semidirect |
| 194. C47 | #11885 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20252969 | 2 |
| C2×C22⋊(C47⋊C16) | 2 |
| #20241399 | 2 |
| #20241396 | 2 |
| C47×#1807 | 2 |
| #11885 | 47 |