Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
434 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 434 conjugacy classes of subgroups — too many to draw. Only its 97 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. #20243436 | C2 | semidirect |
| 4. #20243432 | C2 | semidirect |
| 5. #20241518 | C2 | semidirect |
| 6. #20241516 | C2 | semidirect |
| 9. C23×C47⋊C8 | C4 | semidirect |
| 16. #15689150 | C4 | semidirect |
| 20. #15689087 | C4 | semidirect |
| 21. #15689079 | C4 | semidirect |
| 238. C47 | #12805 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20252083 | 2 |
| #20245029 | 2 |
| #20243436 | 2 |
| #20243432 | 2 |
| #20241518 | 2 |
| #20241516 | 2 |
| C47×#2120 | 2 |
| #12805 | 47 |