Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
294 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 294 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 |
|---|---|---|
| 2. M64×D47 | C2 | semidirect |
| 3. #20245171 | C2 | semidirect |
| 4. #20241576 | C2 | semidirect |
| 5. #20241575 | C2 | semidirect |
| 6. #20241574 | C2 | semidirect |
| 7. C47×#1418 | C2 | semidirect |
| 9. #15689556 | C4 | semidirect |
| 13. #15689552 | C4 | semidirect |
| 14. Q32×D47 | C4 | semidirect |
| 16. D16×D47 | C4 | semidirect |
| 19. #15688957 | C22 | semidirect |
| 22. #15688951 | C22 | semidirect |
| 25. C47×M64 | C22 | semidirect |
| 26. C47×#367 | C22 | semidirect |
| 146. #1418 | D47 | semidirect |
| 167. M64 | C2×D47 | semidirect |
| 170. #367 | C2×D47 | semidirect |
| 172. C47 | #13622 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #508×D47 | 2 |
| M64×D47 | 2 |
| #20245171 | 2 |
| #20241576 | 2 |
| #20241575 | 2 |
| #20241574 | 2 |
| C47×#1418 | 2 |
| #13622 | 47 |