Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
636 conjugacy classes of subgroups; only the 351 normal subgroups are shown.
This group has 636 conjugacy classes of subgroups — too many to draw. Only its 351 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 |
|---|---|---|
| 3. #20245160 | C2 | semidirect |
| 4. C2×#15688945 | C2 | semidirect |
| 7. #15689540 | C4 | semidirect |
| 20. #13093964 | C2×C4 | semidirect |
| 22. C2×C47⋊C16 | C2×C4 | semidirect |
| 101. C47 | #33404 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20256491 | 2 |
| #20251999 | 2 |
| #20245160 | 2 |
| C2×#15688945 | 2 |
| C47×#2912 | 2 |
| #33404 | 47 |