Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
1328 conjugacy classes of subgroups; only the 251 normal subgroups are shown.
This group has 1328 conjugacy classes of subgroups — too many to draw. Only its 251 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. #20258100 | C2 | semidirect |
| 3. #20252085 | C2 | semidirect |
| 4. #20243804 | C2 | semidirect |
| 5. #20243673 | C2 | semidirect |
| 6. #20243191 | C2 | semidirect |
| 7. C47×#1791 | C2 | semidirect |
| 12. C22×C8×D47 | C22 | semidirect |
| 18. #15689149 | C22 | semidirect |
| 20. #15689086 | C22 | semidirect |
| 21. #15689081 | C22 | semidirect |
| 22. #15688895 | C22 | semidirect |
| 34. C2×#10625329 | D4 | semidirect |
| 37. C22×C47⋊C8 | D4 | semidirect |
| 146. #1791 | D47 | semidirect |
| 170. C47 | #21483 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20258100 | 2 |
| #20252780 | 2 |
| #20252085 | 2 |
| #20243804 | 2 |
| #20243673 | 2 |
| #20243191 | 2 |
| C47×#1791 | 2 |
| #21483 | 47 |