Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
470 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 470 conjugacy classes of subgroups — too many to draw. Only its 89 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. C22⋊C16×D47 | C2 | semidirect |
| 3. #20243416 | C2 | semidirect |
| 4. #20241398 | C2 | semidirect |
| 5. #20241397 | C2 | semidirect |
| 6. #20241396 | C2 | semidirect |
| 7. C47×#1347 | C2 | semidirect |
| 8. C2×D8×D47 | C4 | semidirect |
| 12. #15689360 | C4 | semidirect |
| 16. #15689356 | C4 | semidirect |
| 18. #107×D47 | C4 | semidirect |
| 21. C22⋊(C47⋊C16) | C22 | semidirect |
| 23. #15688886 | C22 | semidirect |
| 25. C47×C22⋊C16 | C22 | semidirect |
| 26. C47×#340 | C22 | semidirect |
| 200. #1347 | D47 | semidirect |
| 226. C22⋊C16 | C2×D47 | semidirect |
| 228. #340 | C2×D47 | semidirect |
| 229. C47 | #11886 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #466×D47 | 2 |
| C22⋊C16×D47 | 2 |
| #20243416 | 2 |
| #20241398 | 2 |
| #20241397 | 2 |
| #20241396 | 2 |
| C47×#1347 | 2 |
| #11886 | 47 |