Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
590 conjugacy classes of subgroups; only the 151 normal subgroups are shown.
This group has 590 conjugacy classes of subgroups — too many to draw. Only its 151 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. #20253901 | C2 | semidirect |
| 3. #20245635 | C2 | semidirect |
| 4. #20245634 | C2 | semidirect |
| 5. #20245629 | C2 | semidirect |
| 6. #20245623 | C2 | semidirect |
| 7. #20245092 | C2 | semidirect |
| 8. #346×D47 | C2 | semidirect |
| 9. C47×#2244 | C2 | semidirect |
| 150. #2244 | D47 | semidirect |
| 183. C47 | #33701 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20253901 | 2 |
| #20253815 | 2 |
| #20245635 | 2 |
| #20245634 | 2 |
| #20245629 | 2 |
| #20245623 | 2 |
| #20245092 | 2 |
| #346×D47 | 2 |
| C47×#2244 | 2 |
| #33701 | 47 |