Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
680 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 680 conjugacy classes of subgroups — too many to draw. Only its 171 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. #20252256 | C2 | semidirect |
| 4. #20245452 | C2 | semidirect |
| 5. #20245436 | C2 | semidirect |
| 6. #20245146 | C2 | semidirect |
| 7. #20245108 | C2 | semidirect |
| 9. C22×Q32×C47 | C2 | semidirect |
| 169. C22×Q32 | D47 | semidirect |
| 206. C47 | #33588 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15689564 | 2 |
| #20253877 | 2 |
| #20252256 | 2 |
| #20245452 | 2 |
| #20245436 | 2 |
| #20245146 | 2 |
| #20245108 | 2 |
| #20245096 | 2 |
| C22×Q32×C47 | 2 |
| #33588 | 47 |