Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
462 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 111 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. #346×D47 | C2 | semidirect |
| 3. #334×D47 | C2 | semidirect |
| 4. #20241356 | C2 | semidirect |
| 5. #20241355 | C2 | semidirect |
| 6. #20241354 | C2 | semidirect |
| 7. C47×#1333 | C2 | semidirect |
| 20. #15688899 | C22 | semidirect |
| 22. #15688874 | C22 | semidirect |
| 25. C47×#346 | C22 | semidirect |
| 26. C47×#334 | C22 | semidirect |
| 32. D8×D47 | C8 | semidirect |
| 79. D8×C47 | C2×C8 | semidirect |
| 99. D376 | C2×C8 | semidirect |
| 168. #1333 | D47 | direct (N × H) |
| 174. D47 | #1333 | direct (N × H) |
| 190. #346 | C2×D47 | semidirect |
| 193. #334 | C2×D47 | semidirect |
| 194. C47 | C2×#1333 | semidirect |
| 250. D8 | C8×D47 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×D8×D47 | 2 |
| #346×D47 | 2 |
| #334×D47 | 2 |
| #20241356 | 2 |
| #20241355 | 2 |
| #20241354 | 2 |
| C47×#1333 | 2 |
| C2×#1333 | 47 |