Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
512 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 127 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 |
|---|---|---|
| 1. #20254031 | C2 | semidirect |
| 2. #20245548 | C2 | semidirect |
| 3. #20245543 | C2 | semidirect |
| 4. #20245489 | C2 | semidirect |
| 5. #20245474 | C2 | semidirect |
| 6. #20245422 | C2 | semidirect |
| 7. #20245421 | C2 | semidirect |
| 8. #20245146 | C2 | semidirect |
| 9. C47×#2215 | C2 | semidirect |
| 151. #2215 | D47 | semidirect |
| 186. C47 | #33825 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20254031 | 2 |
| #20245548 | 2 |
| #20245543 | 2 |
| #20245489 | 2 |
| #20245474 | 2 |
| #20245422 | 2 |
| #20245421 | 2 |
| #20245146 | 2 |
| C47×#2215 | 2 |
| #33825 | 47 |