Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
412 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 412 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. #20241836 | C2 | semidirect |
| 5. #20241731 | C2 | semidirect |
| 6. C47⋊#1308 | C2 | semidirect |
| 7. C47×#1291 | C2 | semidirect |
| 196. #1291 | D47 | semidirect |
| 229. C47 | #9531 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20253561 | 2 |
| #20252373 | 2 |
| #20242017 | 2 |
| #20241836 | 2 |
| #20241731 | 2 |
| C47⋊#1308 | 2 |
| C47×#1291 | 2 |
| #9531 | 47 |