Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
504 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 99 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. #20252444 | C2 | semidirect |
| 3. C2×#15688856 | C2 | semidirect |
| 4. #20241749 | C2 | semidirect |
| 5. #20241275 | C2 | semidirect |
| 6. #20241231 | C2 | semidirect |
| 7. C47×#1504 | C2 | semidirect |
| 9. #15689456 | C4 | semidirect |
| 11. #15689439 | C4 | semidirect |
| 14. #15689273 | C4 | semidirect |
| 16. #15689256 | C4 | semidirect |
| 238. #1504 | D47 | semidirect |
| 280. C47 | #9264 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20254149 | 2 |
| #20252444 | 2 |
| C2×#15688856 | 2 |
| #20241749 | 2 |
| #20241275 | 2 |
| #20241231 | 2 |
| C47×#1504 | 2 |
| #9264 | 47 |