Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
434 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 434 conjugacy classes of subgroups — too many to draw. Only its 99 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 |
|---|---|---|
| 3. #20243438 | C2 | semidirect |
| 4. #20241516 | C2 | semidirect |
| 5. C47×#1812 | C2 | semidirect |
| 6. C22×C8×D47 | C4 | semidirect |
| 13. #15689151 | C4 | semidirect |
| 16. #15689086 | C4 | semidirect |
| 17. #15689078 | C4 | semidirect |
| 184. #1812 | D47 | semidirect |
| 211. C47 | #12805 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20252080 | 2 |
| #20245027 | 2 |
| #20243438 | 2 |
| #20241516 | 2 |
| C47×#1812 | 2 |
| #12805 | 47 |