Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
584 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 584 conjugacy classes of subgroups — too many to draw. Only its 171 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. C2×#15689161 | C2 | semidirect |
| 3. #20245597 | C2 | semidirect |
| 4. #20245580 | C2 | semidirect |
| 5. #20245176 | C2 | semidirect |
| 6. #20245101 | C2 | semidirect |
| 7. C47×#2112 | C2 | semidirect |
| 20. #15688951 | C22 | semidirect |
| 21. #15688949 | C22 | semidirect |
| 22. #15688928 | C22 | semidirect |
| 23. #15688925 | C22 | semidirect |
| 145. #2112 | D47 | semidirect |
| 170. C47 | #33647 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20252969 | 2 |
| C2×#15689161 | 2 |
| #20245597 | 2 |
| #20245580 | 2 |
| #20245176 | 2 |
| #20245101 | 2 |
| C47×#2112 | 2 |
| #33647 | 47 |