Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
222 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 222 conjugacy classes of subgroups — too many to draw. Only its 71 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. #20242998 | C2 | semidirect |
| 4. #20241458 | C2 | semidirect |
| 5. #20241447 | C2 | semidirect |
| 6. #20241444 | C2 | semidirect |
| 126. C47 | #12449 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20245535 | 2 |
| #20245525 | 2 |
| #20242998 | 2 |
| #20241458 | 2 |
| #20241447 | 2 |
| #20241444 | 2 |
| C8×D8×C47 | 2 |
| #12449 | 47 |