Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
486 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 486 conjugacy classes of subgroups — too many to draw. Only its 127 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 |
|---|---|---|
| 4. C2×#15688900 | C2 | semidirect |
| 5. #20243275 | C2 | semidirect |
| 6. #20241495 | C2 | semidirect |
| 7. C47×#1383 | C2 | semidirect |
| 12. #15689234 | C4 | semidirect |
| 17. #15688935 | C4 | semidirect |
| 18. #15688925 | C4 | semidirect |
| 39. #13093964 | C2×C4 | semidirect |
| 41. #13093958 | C2×C4 | semidirect |
| 53. C2×C16×C47 | C2×C4 | semidirect |
| 55. #108×C47 | C2×C4 | semidirect |
| 147. #1383 | D47 | semidirect |
| 169. C47 | #12647 | semidirect |
| 192. C2×C16 | C4×D47 | semidirect |
| 194. #108 | C4×D47 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15689234 | 2 |
| C2×#15688935 | 2 |
| #20245105 | 2 |
| C2×#15688900 | 2 |
| #20243275 | 2 |
| #20241495 | 2 |
| C47×#1383 | 2 |
| #12647 | 47 |