Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
716 conjugacy classes of subgroups; only the 163 normal subgroups are shown.
This group has 716 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 |
|---|---|---|
| 2. C22×#13093969 | C2 | semidirect |
| 3. #20253883 | C2 | semidirect |
| 4. #20252239 | C2 | semidirect |
| 5. #20245442 | C2 | semidirect |
| 6. #20245432 | C2 | semidirect |
| 7. #20245146 | C2 | semidirect |
| 8. #20245107 | C2 | semidirect |
| 9. C47×#2138 | C2 | semidirect |
| 22. #15689506 | C22 | semidirect |
| 23. #15689501 | C22 | semidirect |
| 28. Dic47⋊C16 | C22 | semidirect |
| 29. #15688926 | C22 | semidirect |
| 33. C47×#358 | C22 | semidirect |
| 34. C47×#357 | C22 | semidirect |
| 180. #2138 | D47 | semidirect |
| 209. #358 | C2×D47 | semidirect |
| 210. #357 | C2×D47 | semidirect |
| 211. C47 | #33586 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15689558 | 2 |
| C22×#13093969 | 2 |
| #20253883 | 2 |
| #20252239 | 2 |
| #20245442 | 2 |
| #20245432 | 2 |
| #20245146 | 2 |
| #20245107 | 2 |
| C47×#2138 | 2 |
| #33586 | 47 |