Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
564 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 131 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. #20254126 | C2 | semidirect |
| 2. #20252299 | C2 | semidirect |
| 3. #20245603 | C2 | semidirect |
| 4. #20245560 | C2 | semidirect |
| 5. #20245465 | C2 | semidirect |
| 6. #20245336 | C2 | semidirect |
| 7. #20245288 | C2 | semidirect |
| 8. C47×#2165 | C2 | semidirect |
| 13. #15689521 | C22 | semidirect |
| 14. #15689500 | C22 | semidirect |
| 23. #15689236 | C22 | semidirect |
| 26. #15688946 | C22 | semidirect |
| 27. #15688937 | C22 | semidirect |
| 30. C47×#364 | C22 | semidirect |
| 32. C47×#347 | C22 | semidirect |
| 105. Dic188 | #41 | semidirect |
| 109. D376 | #41 | semidirect |
| 172. #2165 | D47 | semidirect |
| 197. #364 | C2×D47 | semidirect |
| 201. #347 | C2×D47 | semidirect |
| 202. C47 | #33688 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20254126 | 2 |
| #20252299 | 2 |
| #20245603 | 2 |
| #20245560 | 2 |
| #20245465 | 2 |
| #20245336 | 2 |
| #20245288 | 2 |
| C47×#2165 | 2 |
| #33688 | 47 |