Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
550 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 550 conjugacy classes of subgroups — too many to draw. Only its 97 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 |
|---|---|---|
| 1. #20253392 | C2 | semidirect |
| 3. #20244186 | C2 | semidirect |
| 4. #20241791 | C2 | semidirect |
| 5. #20241787 | C2 | semidirect |
| 6. #20241219 | C2 | semidirect |
| 7. C47×#3135 | C2 | semidirect |
| 200. #3135 | D47 | semidirect |
| 238. C47 | #10033 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20253392 | 2 |
| #20253384 | 2 |
| #20244186 | 2 |
| #20241791 | 2 |
| #20241787 | 2 |
| #20241219 | 2 |
| C47×#3135 | 2 |
| #10033 | 47 |