Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
380 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 105 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×#15688952 | C2 | semidirect |
| 5. #20241501 | C2 | semidirect |
| 6. #20241477 | C2 | semidirect |
| 7. C47×#1953 | C2 | semidirect |
| 18. #15688929 | C4 | semidirect |
| 140. #1953 | D47 | semidirect |
| 164. C47 | #12947 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20252306 | 2 |
| C2×#15688952 | 2 |
| #20245115 | 2 |
| C2×#15688929 | 2 |
| #20241501 | 2 |
| #20241477 | 2 |
| C47×#1953 | 2 |
| #12947 | 47 |