Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
748 conjugacy classes of subgroups; only the 163 normal subgroups are shown.
This group has 748 conjugacy classes of subgroups — too many to draw. Only its 163 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 |
|---|---|---|
| 1. C2×#15689558 | C2 | semidirect |
| 2. C22×D752 | C2 | semidirect |
| 3. #20253875 | C2 | semidirect |
| 4. #20252239 | C2 | semidirect |
| 5. #20245446 | C2 | semidirect |
| 6. #20245422 | C2 | semidirect |
| 7. #20245146 | C2 | semidirect |
| 8. #20245103 | C2 | semidirect |
| 9. C47×#2138 | C2 | semidirect |
| 16. C2×#13093967 | C22 | semidirect |
| 19. C2×#13093965 | C22 | semidirect |
| 22. #15689508 | C22 | semidirect |
| 23. #15689498 | C22 | semidirect |
| 25. #15689205 | C22 | semidirect |
| 28. Dic47⋊C16 | C22 | semidirect |
| 29. #15688923 | C22 | semidirect |
| 33. C47×#358 | C22 | semidirect |
| 34. C47×#357 | C22 | semidirect |
| 44. C2×D376 | D4 | semidirect |
| 184. #2138 | D47 | semidirect |
| 213. #358 | C2×D47 | semidirect |
| 215. #357 | C2×D47 | semidirect |
| 216. C47 | #33585 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15689558 | 2 |
| C22×D752 | 2 |
| #20253875 | 2 |
| #20252239 | 2 |
| #20245446 | 2 |
| #20245422 | 2 |
| #20245146 | 2 |
| #20245103 | 2 |
| C47×#2138 | 2 |
| #33585 | 47 |