Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
426 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 426 conjugacy classes of subgroups — too many to draw. Only its 119 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. #20245191 | C2 | semidirect |
| 2. #20242144 | C2 | semidirect |
| 3. #20241355 | C2 | semidirect |
| 8. #15688899 | C22 | semidirect |
| 10. #15688874 | C22 | semidirect |
| 60. D8×C47 | M16 | semidirect |
| 146. C47 | #11663 | semidirect |
| 187. D8 | #10625329 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20245191 | 2 |
| #20242144 | 2 |
| #20241355 | 2 |
| C2×C4×D8×C47 | 2 |
| #11663 | 47 |