Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
442 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 442 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. #20245643 | C2 | semidirect |
| 2. #20245433 | C2 | semidirect |
| 3. #20242753 | C2 | semidirect |
| 4. #20241434 | C2 | semidirect |
| 5. #20241349 | C2 | semidirect |
| 6. D4⋊(C47⋊C16) | C2 | semidirect |
| 10. #15689503 | C22 | semidirect |
| 12. C4⋊(C47⋊C16) | C22 | semidirect |
| 14. C4×C47⋊C16 | C22 | semidirect |
| 15. #15688876 | C22 | semidirect |
| 112. D4×C47 | SD32 | semidirect |
| 180. C47 | #12320 | semidirect |
| 270. D4 | #13093968 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20245643 | 2 |
| #20245433 | 2 |
| #20242753 | 2 |
| #20241434 | 2 |
| #20241349 | 2 |
| D4⋊(C47⋊C16) | 2 |
| D4×D8×C47 | 2 |
| #12320 | 47 |