Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
778 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 778 conjugacy classes of subgroups — too many to draw. Only its 143 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 |
|---|---|---|
| 1. #20255200 | C2 | semidirect |
| 2. #20254987 | C2 | semidirect |
| 3. #20242850 | C2 | semidirect |
| 4. #20242822 | C2 | semidirect |
| 5. #20242620 | C2 | semidirect |
| 6. #20242440 | C2 | semidirect |
| 7. #20242274 | C2 | semidirect |
| 8. C8×D376 | C2 | semidirect |
| 9. C47×#1706 | C2 | semidirect |
| 12. #15689758 | C22 | semidirect |
| 14. #15689400 | C22 | semidirect |
| 17. #15689325 | C22 | semidirect |
| 25. #15689202 | C22 | semidirect |
| 26. C8×D188 | C22 | semidirect |
| 28. #15688876 | C22 | semidirect |
| 29. #15688876 | C22 | semidirect |
| 30. #15688869 | C22 | semidirect |
| 31. #15688867 | C22 | semidirect |
| 32. #15688852 | C22 | semidirect |
| 33. #15688852 | C22 | semidirect |
| 34. C47×#500 | C22 | semidirect |
| 36. C47×#492 | C22 | semidirect |
| 37. C47×#486 | C22 | semidirect |
| 38. C82×C47 | C22 | semidirect |
| 126. D376 | D8 | semidirect |
| 189. #1706 | D47 | semidirect |
| 205. #500 | C2×D47 | semidirect |
| 207. #492 | C2×D47 | semidirect |
| 208. #486 | C2×D47 | semidirect |
| 230. C82 | C2×D47 | semidirect |
| 231. C47 | #19884 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20255200 | 2 |
| #20254987 | 2 |
| #20242850 | 2 |
| #20242822 | 2 |
| #20242620 | 2 |
| #20242440 | 2 |
| #20242274 | 2 |
| C8×D376 | 2 |
| C47×#1706 | 2 |
| #19884 | 47 |