Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
290 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 290 conjugacy classes of subgroups — too many to draw. Only its 75 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. #20245423 | C2 | semidirect |
| 2. #20243003 | C2 | semidirect |
| 3. #20241458 | C2 | semidirect |
| 4. #20241433 | C2 | semidirect |
| 5. C8×D8×C47 | C2 | semidirect |
| 41. D8×C47 | D8 | semidirect |
| 78. C8×C47 | D16 | semidirect |
| 97. C8×D8 | D47 | semidirect |
| 116. C47 | #12424 | semidirect |
| 147. D8 | D376 | semidirect |
| 178. C8 | #13093965 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20245423 | 2 |
| #20243003 | 2 |
| #20241458 | 2 |
| #20241433 | 2 |
| C8×D8×C47 | 2 |
| #12424 | 47 |