Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
126 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 126 conjugacy classes of subgroups — too many to draw. Only its 47 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. #20241605 | C2 | semidirect |
| 3. #20241602 | C2 | semidirect |
| 4. #20241599 | C2 | semidirect |
| 5. C2×C47×Q64 | C2 | semidirect |
| 53. C2×Q64 | D47 | semidirect |
| 69. C47 | #13743 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20245697 | 2 |
| #20241605 | 2 |
| #20241602 | 2 |
| #20241599 | 2 |
| C2×C47×Q64 | 2 |
| #13743 | 47 |