Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
1306 conjugacy classes of subgroups; only the 291 normal subgroups are shown.
This group has 1306 conjugacy classes of subgroups — too many to draw. Only its 291 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 |
| 2. #20252092 | C2 | semidirect |
| 3. #20243807 | C2 | semidirect |
| 4. #20243676 | C2 | semidirect |
| 5. #20243339 | C2 | semidirect |
| 6. #20243190 | C2 | semidirect |
| 12. C22×#10625329 | C22 | semidirect |
| 15. #15689150 | C22 | semidirect |
| 18. #15689087 | C22 | semidirect |
| 19. #15689079 | C22 | semidirect |
| 20. #15688893 | C22 | semidirect |
| 35. C2×#10625329 | D4 | semidirect |
| 39. C22×C47⋊C8 | D4 | semidirect |
| 170. C47 | #21484 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20258100 | 2 |
| #20252092 | 2 |
| #20243807 | 2 |
| #20243676 | 2 |
| #20243339 | 2 |
| #20243190 | 2 |
| C47×#3025 | 2 |
| #21484 | 47 |