Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
422 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 422 conjugacy classes of subgroups — too many to draw. Only its 101 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. #20245190 | C2 | semidirect |
| 3. #20245185 | C2 | semidirect |
| 4. #20241344 | C2 | semidirect |
| 5. D4⋊(C47⋊C16) | C2 | semidirect |
| 6. #20241342 | C2 | semidirect |
| 7. C47×D4⋊C16 | C2 | semidirect |
| 18. C4⋊(C47⋊C16) | C22 | semidirect |
| 23. C4×C47⋊C16 | C22 | semidirect |
| 25. C47×C4⋊C16 | C22 | semidirect |
| 26. C4×C16×C47 | C22 | semidirect |
| 175. D4⋊C16 | D47 | semidirect |
| 195. C4⋊C16 | C2×D47 | semidirect |
| 200. C4×C16 | C2×D47 | semidirect |
| 201. C47 | #11631 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C8×D4×D47 | 2 |
| #20245190 | 2 |
| #20245185 | 2 |
| #20241344 | 2 |
| D4⋊(C47⋊C16) | 2 |
| #20241342 | 2 |
| C47×D4⋊C16 | 2 |
| #11631 | 47 |