Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
440 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 440 conjugacy classes of subgroups — too many to draw. Only its 85 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 |
|---|---|---|
| 4. #20241407 | C2 | semidirect |
| 5. #20241406 | C2 | semidirect |
| 6. #20241405 | C2 | semidirect |
| 7. C47×#1350 | C2 | semidirect |
| 178. #1350 | D47 | semidirect |
| 204. C47 | #11712 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #467×D47 | 2 |
| #20244997 | 2 |
| #341×D47 | 2 |
| #20241407 | 2 |
| #20241406 | 2 |
| #20241405 | 2 |
| C47×#1350 | 2 |
| #11712 | 47 |