Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
234 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 69 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 |
|---|---|---|
| 2. #20243005 | C2 | semidirect |
| 4. #20241457 | C2 | semidirect |
| 5. #20241446 | C2 | semidirect |
| 6. #20241445 | C2 | semidirect |
| 49. D8×C47 | Q16 | semidirect |
| 126. C47 | #12447 | semidirect |
| 154. D8 | #10625337 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20245535 | 2 |
| #20243005 | 2 |
| D8×C47⋊C8 | 2 |
| #20241457 | 2 |
| #20241446 | 2 |
| #20241445 | 2 |
| C47×#2226 | 2 |
| #12447 | 47 |