Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
252 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 252 conjugacy classes of subgroups — too many to draw. Only its 69 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. #20245644 | C2 | semidirect |
| 2. C16×D188 | C2 | semidirect |
| 3. #20242754 | C2 | semidirect |
| 5. #20241436 | C2 | semidirect |
| 6. #20241433 | C2 | semidirect |
| 7. C47×#1372 | C2 | semidirect |
| 72. C16×C47 | D8 | semidirect |
| 87. D188 | SD32 | semidirect |
| 117. #1372 | D47 | semidirect |
| 140. C47 | #12432 | semidirect |
| 191. C16 | D376 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20245644 | 2 |
| C16×D188 | 2 |
| #20242754 | 2 |
| #20242744 | 2 |
| #20241436 | 2 |
| #20241433 | 2 |
| C47×#1372 | 2 |
| #12432 | 47 |