Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
552 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 101 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. C22×#13093968 | C2 | semidirect |
| 2. C2×#15689398 | C2 | semidirect |
| 3. C2×#15688936 | C2 | semidirect |
| 4. #20245107 | C2 | semidirect |
| 5. C2×#15688907 | C2 | semidirect |
| 6. #20241483 | C2 | semidirect |
| 37. C2×Dic188 | D4 | semidirect |
| 47. C2×C47⋊C16 | D4 | semidirect |
| 49. #13093960 | D4 | semidirect |
| 223. C47 | #13321 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13093968 | 2 |
| C2×#15689398 | 2 |
| C2×#15688936 | 2 |
| #20245107 | 2 |
| C2×#15688907 | 2 |
| #20241483 | 2 |
| C47×#3058 | 2 |
| #13321 | 47 |