Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
712 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 712 conjugacy classes of subgroups — too many to draw. Only its 97 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. #20251838 | C2 | semidirect |
| 3. #20243333 | C2 | semidirect |
| 4. #20241748 | C2 | semidirect |
| 5. #20241264 | C2 | semidirect |
| 6. #20241236 | C2 | semidirect |
| 7. C47×#1507 | C2 | semidirect |
| 9. C22×#10625335 | C4 | semidirect |
| 10. C22×#10625334 | C4 | semidirect |
| 18. C2×#13093947 | C4 | semidirect |
| 19. C2×#13093944 | C4 | semidirect |
| 275. #1507 | D47 | semidirect |
| 314. C47 | #9241 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15689266 | 2 |
| #20251838 | 2 |
| #20243333 | 2 |
| #20241748 | 2 |
| #20241264 | 2 |
| #20241236 | 2 |
| C47×#1507 | 2 |
| #9241 | 47 |