Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
224 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 85 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. #20242285 | C2 | semidirect |
| 3. #20241462 | C2 | semidirect |
| 4. #20241352 | C2 | semidirect |
| 6. C16×C47⋊C8 | C2 | semidirect |
| 66. C16×C47 | M16 | semidirect |
| 88. C47⋊C8 | SD32 | semidirect |
| 128. C47 | #12082 | semidirect |
| 173. C16 | #10625329 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20242285 | 2 |
| #20242273 | 2 |
| #20241462 | 2 |
| #20241352 | 2 |
| #20241349 | 2 |
| C16×C47⋊C8 | 2 |
| C4×SD32×C47 | 2 |
| #12082 | 47 |