Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
598 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 598 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 |
|---|---|---|
| 2. #20253845 | C2 | semidirect |
| 3. #20242114 | C2 | semidirect |
| 4. #20241986 | C2 | semidirect |
| 5. #20241895 | C2 | semidirect |
| 6. #20241281 | C2 | semidirect |
| 7. C47×#2640 | C2 | semidirect |
| 187. #2640 | D47 | semidirect |
| 221. C47 | #10090 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20254375 | 2 |
| #20253845 | 2 |
| #20242114 | 2 |
| #20241986 | 2 |
| #20241895 | 2 |
| #20241281 | 2 |
| C47×#2640 | 2 |
| #10090 | 47 |