Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
226 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 226 conjugacy classes of subgroups — too many to draw. Only its 71 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. #20242303 | C2 | semidirect |
| 3. #20241454 | C2 | semidirect |
| 4. #20241356 | C2 | semidirect |
| 5. C47×#1313 | C2 | semidirect |
| 43. C16×C47 | M16 | semidirect |
| 70. #1313 | D47 | semidirect |
| 84. C47 | #12089 | semidirect |
| 112. C16 | #10625324 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20245265 | 2 |
| #20242303 | 2 |
| #20241454 | 2 |
| #20241356 | 2 |
| C47×#1313 | 2 |
| #12089 | 47 |