Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
488 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 488 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 |
|---|---|---|
| 3. #20253768 | C2 | semidirect |
| 5. #20241810 | C2 | semidirect |
| 6. #20241277 | C2 | semidirect |
| 7. C47×#1997 | C2 | semidirect |
| 176. #1997 | D47 | semidirect |
| 208. C47 | #10114 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20254776 | 2 |
| #20254313 | 2 |
| #20253768 | 2 |
| #20241979 | 2 |
| #20241810 | 2 |
| #20241277 | 2 |
| C47×#1997 | 2 |
| #10114 | 47 |