Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
642 conjugacy classes of subgroups; only the 207 normal subgroups are shown.
This group has 642 conjugacy classes of subgroups — too many to draw. Only its 207 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. #20252304 | C2 | semidirect |
| 3. #20245273 | C2 | semidirect |
| 4. #20245268 | C2 | semidirect |
| 5. C2×#15688929 | C2 | semidirect |
| 6. #20244987 | C2 | semidirect |
| 7. C47×#2161 | C2 | semidirect |
| 10. #15689566 | C4 | semidirect |
| 11. #15689561 | C4 | semidirect |
| 15. #15689239 | C22 | semidirect |
| 18. #15688929 | C22 | semidirect |
| 19. #15688929 | C22 | semidirect |
| 20. #15688898 | C22 | semidirect |
| 21. C16×Dic47 | C22 | semidirect |
| 24. C47×#368 | C22 | semidirect |
| 121. #2161 | D47 | semidirect |
| 140. #368 | C2×D47 | semidirect |
| 145. C47 | #33464 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20256524 | 2 |
| #20252304 | 2 |
| #20245273 | 2 |
| #20245268 | 2 |
| C2×#15688929 | 2 |
| #20244987 | 2 |
| C47×#2161 | 2 |
| #33464 | 47 |