Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
460 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 111 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. #20244333 | C2 | semidirect |
| 4. C4×#13093957 | C2 | semidirect |
| 6. #20241678 | C2 | semidirect |
| 7. C47×#1503 | C2 | semidirect |
| 9. #15689519 | C4 | semidirect |
| 10. #15689497 | C4 | semidirect |
| 11. #15689473 | C4 | semidirect |
| 12. #15689471 | C4 | semidirect |
| 163. C47⋊C8 | #104 | semidirect |
| 189. #1503 | D47 | semidirect |
| 221. C47 | #9722 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20253948 | 2 |
| #20244333 | 2 |
| #20244306 | 2 |
| C4×#13093957 | 2 |
| #20241884 | 2 |
| #20241678 | 2 |
| C47×#1503 | 2 |
| #9722 | 47 |