Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
460 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 109 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. C2×#15688947 | C2 | semidirect |
| 5. #20241493 | C2 | semidirect |
| 6. #20241468 | C2 | semidirect |
| 7. C47×#1946 | C2 | semidirect |
| 18. #15688923 | C4 | semidirect |
| 41. C2×C47⋊C16 | C2×C4 | semidirect |
| 52. #107×C47 | C2×C4 | semidirect |
| 144. #1946 | D47 | semidirect |
| 168. C47 | #12956 | semidirect |
| 194. #107 | C4×D47 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15689236 | 2 |
| C2×#15688947 | 2 |
| C2×#15688935 | 2 |
| #20245103 | 2 |
| #20241493 | 2 |
| #20241468 | 2 |
| C47×#1946 | 2 |
| #12956 | 47 |