Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
478 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 478 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 |
|---|---|---|
| 3. C2×#15688859 | C2 | semidirect |
| 4. #20241753 | C2 | semidirect |
| 5. #20241275 | C2 | semidirect |
| 6. #20241231 | C2 | semidirect |
| 10. #15689451 | C4 | semidirect |
| 11. #15689434 | C4 | semidirect |
| 15. #15689278 | C4 | semidirect |
| 16. #15689261 | C4 | semidirect |
| 268. C47 | #9263 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20254165 | 2 |
| #20252444 | 2 |
| C2×#15688859 | 2 |
| #20241753 | 2 |
| #20241275 | 2 |
| #20241231 | 2 |
| C47×#1504 | 2 |
| #9263 | 47 |