Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
450 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 450 conjugacy classes of subgroups — too many to draw. Only its 105 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. #20244981 | C2 | semidirect |
| 3. #20242133 | C2 | semidirect |
| 4. #20241356 | C2 | semidirect |
| 5. #20241355 | C2 | semidirect |
| 6. #20241354 | C2 | semidirect |
| 7. C47×#1333 | C2 | semidirect |
| 20. #15688899 | C22 | semidirect |
| 23. #15688874 | C22 | semidirect |
| 25. C47×#346 | C22 | semidirect |
| 26. C47×#334 | C22 | semidirect |
| 32. D8×D47 | C8 | semidirect |
| 167. #1333 | D47 | semidirect |
| 188. #346 | C2×D47 | semidirect |
| 192. #334 | C2×D47 | semidirect |
| 193. C47 | #11599 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×D8×D47 | 2 |
| #20244981 | 2 |
| #20242133 | 2 |
| #20241356 | 2 |
| #20241355 | 2 |
| #20241354 | 2 |
| C47×#1333 | 2 |
| #11599 | 47 |