Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
522 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 522 conjugacy classes of subgroups — too many to draw. Only its 107 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. #20252188 | C2 | semidirect |
| 3. C2×#15688934 | C2 | semidirect |
| 4. #20244265 | C2 | semidirect |
| 5. #20241493 | C2 | semidirect |
| 6. #20241471 | C2 | semidirect |
| 7. C47×#2140 | C2 | semidirect |
| 11. #15689559 | C4 | semidirect |
| 48. #13093964 | C2×C4 | semidirect |
| 63. C2×D8×C47 | C2×C4 | semidirect |
| 115. Dic188 | C22⋊C4 | semidirect |
| 117. D376 | C22⋊C4 | semidirect |
| 182. #2140 | D47 | semidirect |
| 212. C47 | #13025 | semidirect |
| 227. C2×D8 | C4×D47 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15689559 | 2 |
| #20252188 | 2 |
| C2×#15688934 | 2 |
| #20244265 | 2 |
| #20241493 | 2 |
| #20241471 | 2 |
| C47×#2140 | 2 |
| #13025 | 47 |