Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
4614 conjugacy classes of subgroups; only the 667 normal subgroups are shown.
This group has 4614 conjugacy classes of subgroups — too many to draw. Only its 667 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. C2×C4×C22⋊Dic47 | C2 | semidirect |
| 2. #20241659 | C2 | semidirect |
| 3. #20241629 | C2 | semidirect |
| 10. C22×#41×C47 | C4 | semidirect |
| 46. C22×C4×C47 | C22⋊C4 | semidirect |
| 53. C22×Dic47 | #41 | semidirect |
| 100. C22×#41 | Dic47 | semidirect |
| 108. C47 | #13851 | semidirect |
| 144. C22×C4 | C22⋊Dic47 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×C22⋊Dic47 | 2 |
| #20241659 | 2 |
| #20241629 | 2 |
| C23×#41×C47 | 2 |
| #13851 | 47 |