Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
912 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 912 conjugacy classes of subgroups — too many to draw. Only its 109 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. #20252414 | C2 | semidirect |
| 3. #20243373 | C2 | semidirect |
| 4. #20243319 | C2 | semidirect |
| 5. #20241256 | C2 | semidirect |
| 6. #20241255 | C2 | semidirect |
| 7. C47×#1786 | C2 | semidirect |
| 18. #15689037 | C4 | semidirect |
| 19. #15689031 | C4 | semidirect |
| 33. C22×C47⋊C8 | D4 | semidirect |
| 70. C22×C8×C47 | D4 | semidirect |
| 273. #1786 | D47 | semidirect |
| 308. C47 | #9472 | semidirect |
| 323. C22×C8 | C22⋊D47 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20252414 | 2 |
| #20246738 | 2 |
| #20243373 | 2 |
| #20243319 | 2 |
| #20241256 | 2 |
| #20241255 | 2 |
| C47×#1786 | 2 |
| #9472 | 47 |