Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
234 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 77 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. #20242302 | C2 | semidirect |
| 2. #20242212 | C2 | semidirect |
| 3. #20241454 | C2 | semidirect |
| 4. #20241355 | C2 | semidirect |
| 5. #20241355 | C2 | semidirect |
| 6. #20241310 | C2 | semidirect |
| 51. D8×C47 | M16 | semidirect |
| 131. C47 | #12078 | semidirect |
| 160. D8 | #10625329 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20242302 | 2 |
| #20242212 | 2 |
| #20241454 | 2 |
| #20241355 | 2 |
| #20241310 | 2 |
| C47×#2177 | 2 |
| #12078 | 47 |