Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
226 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 226 conjugacy classes of subgroups — too many to draw. Only its 91 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. #20245296 | C2 | semidirect |
| 3. #20241451 | C2 | semidirect |
| 4. #20241366 | C2 | semidirect |
| 6. #20241304 | C2 | semidirect |
| 65. C16×C47 | SD16 | semidirect |
| 128. C47 | #12049 | semidirect |
| 173. C16 | #10625335 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20245296 | 2 |
| C8×#10625335 | 2 |
| #20241451 | 2 |
| #20241366 | 2 |
| D4⋊(C47⋊C16) | 2 |
| #20241304 | 2 |
| D4×C16×C47 | 2 |
| #12049 | 47 |