Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
572 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 572 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×#13093965 | C2 | semidirect |
| 2. C2×#15689393 | C2 | semidirect |
| 3. C2×#15688936 | C2 | semidirect |
| 4. #20245103 | C2 | semidirect |
| 5. C2×#15688907 | C2 | semidirect |
| 6. #20241483 | C2 | semidirect |
| 7. C47×#3058 | C2 | semidirect |
| 38. C2×D376 | D4 | semidirect |
| 47. C2×C47⋊C16 | D4 | semidirect |
| 49. #13093960 | D4 | semidirect |
| 195. #3058 | D47 | semidirect |
| 228. C47 | #13319 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13093965 | 2 |
| C2×#15689393 | 2 |
| C2×#15688936 | 2 |
| #20245103 | 2 |
| C2×#15688907 | 2 |
| #20241483 | 2 |
| C47×#3058 | 2 |
| #13319 | 47 |