Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
416 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 81 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. #20244997 | C2 | semidirect |
| 3. #20243416 | C2 | semidirect |
| 4. #20241401 | C2 | semidirect |
| 5. #20241399 | C2 | semidirect |
| 6. #20241397 | C2 | semidirect |
| 7. C47×#1347 | C2 | semidirect |
| 8. C2×#13094043 | C4 | semidirect |
| 12. #15689365 | C4 | semidirect |
| 14. #15689356 | C4 | semidirect |
| 17. #15689160 | C4 | semidirect |
| 189. #1347 | D47 | semidirect |
| 217. C47 | #11890 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20252967 | 2 |
| #20244997 | 2 |
| #20243416 | 2 |
| #20241401 | 2 |
| #20241399 | 2 |
| #20241397 | 2 |
| C47×#1347 | 2 |
| #11890 | 47 |