Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
212 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 212 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. #20245225 | C2 | semidirect |
| 3. #20245224 | C2 | semidirect |
| 4. #20241463 | C2 | semidirect |
| 5. #20241362 | C2 | semidirect |
| 6. #20241305 | C2 | semidirect |
| 7. C47×#1335 | C2 | semidirect |
| 25. #13093970 | C8 | semidirect |
| 26. #13093968 | C8 | semidirect |
| 27. #13093967 | C8 | semidirect |
| 28. #13093965 | C8 | semidirect |
| 104. #1335 | D47 | semidirect |
| 125. C47 | #12047 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20245267 | 2 |
| #20245225 | 2 |
| #20245224 | 2 |
| #20241463 | 2 |
| #20241362 | 2 |
| #20241305 | 2 |
| C47×#1335 | 2 |
| #12047 | 47 |