Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
552 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 87 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. #20254333 | C2 | semidirect |
| 4. #20244377 | C2 | semidirect |
| 6. #20241278 | C2 | semidirect |
| 7. C47×#1526 | C2 | semidirect |
| 180. #1526 | D47 | semidirect |
| 211. C47 | #10107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20254771 | 2 |
| #20254333 | 2 |
| #20253847 | 2 |
| #20244377 | 2 |
| #20241806 | 2 |
| #20241278 | 2 |
| C47×#1526 | 2 |
| #10107 | 47 |