Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
204 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 204 conjugacy classes of subgroups — too many to draw. Only its 75 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. #20245231 | C2 | semidirect |
| 3. #20241455 | C2 | semidirect |
| 4. #20241364 | C2 | semidirect |
| 5. #20241363 | C2 | semidirect |
| 6. #20241310 | C2 | semidirect |
| 7. C47×#2171 | C2 | semidirect |
| 25. #13093970 | C8 | semidirect |
| 26. #13093968 | C8 | semidirect |
| 27. #13093967 | C8 | semidirect |
| 28. #13093965 | C8 | semidirect |
| 100. #2171 | D47 | semidirect |
| 124. C47 | #12068 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20245272 | 2 |
| #20245231 | 2 |
| #20241455 | 2 |
| #20241364 | 2 |
| #20241363 | 2 |
| #20241310 | 2 |
| C47×#2171 | 2 |
| #12068 | 47 |