Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
418 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 418 conjugacy classes of subgroups — too many to draw. Only its 73 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. #20245612 | C2 | semidirect |
| 3. #20245536 | C2 | semidirect |
| 4. #20242787 | C2 | semidirect |
| 5. #20241435 | C2 | semidirect |
| 6. #20241350 | C2 | semidirect |
| 7. C47×D4⋊C16 | C2 | semidirect |
| 10. #15689528 | C22 | semidirect |
| 20. #15688876 | C22 | semidirect |
| 23. C47×C4⋊C16 | C22 | semidirect |
| 24. C4×C16×C47 | C22 | semidirect |
| 150. D4⋊C16 | D47 | semidirect |
| 168. C4⋊C16 | C2×D47 | semidirect |
| 171. C4×C16 | C2×D47 | semidirect |
| 174. C47 | #12372 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×D376 | 2 |
| #20245612 | 2 |
| #20245536 | 2 |
| #20242787 | 2 |
| #20241435 | 2 |
| #20241350 | 2 |
| C47×D4⋊C16 | 2 |
| #12372 | 47 |