Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
394 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 394 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. #20245160 | C2 | semidirect |
| 3. C2×#15688946 | C2 | semidirect |
| 6. #20241493 | C2 | semidirect |
| 7. C47×#1384 | C2 | semidirect |
| 21. #15688906 | C4 | semidirect |
| 42. #13093964 | C2×C4 | semidirect |
| 56. C2×C16×C47 | C2×C4 | semidirect |
| 154. #1384 | D47 | semidirect |
| 178. C47 | #12934 | semidirect |
| 202. C2×C16 | C4×D47 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20251980 | 2 |
| #20245160 | 2 |
| C2×#15688946 | 2 |
| #20245015 | 2 |
| #20243439 | 2 |
| #20241493 | 2 |
| C47×#1384 | 2 |
| #12934 | 47 |