Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
234 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 71 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. #20245612 | C2 | semidirect |
| 2. #20242787 | C2 | semidirect |
| 4. #20241462 | C2 | semidirect |
| 5. #20241445 | C2 | semidirect |
| 6. #20241435 | C2 | semidirect |
| 7. D4×C16×C47 | C2 | semidirect |
| 108. D4×C16 | D47 | semidirect |
| 134. C47 | #12468 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20245612 | 2 |
| #20242787 | 2 |
| #20242743 | 2 |
| #20241462 | 2 |
| #20241445 | 2 |
| #20241435 | 2 |
| D4×C16×C47 | 2 |
| #12468 | 47 |