Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
418 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 418 conjugacy classes of subgroups — too many to draw. Only its 79 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. #20245611 | C2 | semidirect |
| 2. #20245535 | C2 | semidirect |
| 3. #20242787 | C2 | semidirect |
| 4. #20241434 | C2 | semidirect |
| 5. #20241349 | C2 | semidirect |
| 6. D4⋊(C47⋊C16) | C2 | semidirect |
| 8. #15689528 | C22 | semidirect |
| 11. C4⋊(C47⋊C16) | C22 | semidirect |
| 14. C4×C47⋊C16 | C22 | semidirect |
| 15. #15688876 | C22 | semidirect |
| 174. C47 | #12372 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20245611 | 2 |
| #20245535 | 2 |
| #20242787 | 2 |
| #20241434 | 2 |
| #20241349 | 2 |
| D4⋊(C47⋊C16) | 2 |
| D4×D8×C47 | 2 |
| #12372 | 47 |