Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
238 conjugacy classes of subgroups; only the 163 normal subgroups are shown.
This group has 238 conjugacy classes of subgroups — too many to draw. Only its 163 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 |
|---|---|---|
| 3. #20241521 | C2 | semidirect |
| 4. C32×Dic47 | C2 | semidirect |
| 8. #15688957 | C4 | semidirect |
| 13. C2×C32×C47 | C4 | semidirect |
| 75. C2×C32 | Dic47 | semidirect |
| 80. C47 | #13549 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15688957 | 2 |
| #20244984 | 2 |
| #20241521 | 2 |
| C32×Dic47 | 2 |
| C22×C32×C47 | 2 |
| #13549 | 47 |