Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
438 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 438 conjugacy classes of subgroups — too many to draw. Only its 89 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. #20252382 | C2 | semidirect |
| 3. #20242009 | C2 | semidirect |
| 4. C2×#15688862 | C2 | semidirect |
| 5. #20241741 | C2 | semidirect |
| 6. #20241232 | C2 | semidirect |
| 7. C47×#1302 | C2 | semidirect |
| 211. #1302 | D47 | semidirect |
| 247. C47 | #9265 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20254355 | 2 |
| #20252382 | 2 |
| #20242009 | 2 |
| C2×#15688862 | 2 |
| #20241741 | 2 |
| #20241232 | 2 |
| C47×#1302 | 2 |
| #9265 | 47 |