Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
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. #20286527 | C2 | semidirect |
| 2. #20286314 | C2 | semidirect |
| 3. #20274177 | C2 | semidirect |
| 4. #20274149 | C2 | semidirect |
| 5. #20273947 | C2 | semidirect |
| 6. #20273767 | C2 | semidirect |
| 7. #20273601 | C2 | semidirect |
| 8. C8×D424 | C2 | semidirect |
| 9. C53×#1706 | C2 | semidirect |
| 12. #16811258 | C22 | semidirect |
| 14. #16810900 | C22 | semidirect |
| 17. #16810825 | C22 | semidirect |
| 25. #16810702 | C22 | semidirect |
| 26. C8×D212 | C22 | semidirect |
| 28. #16810376 | C22 | semidirect |
| 29. #16810376 | C22 | semidirect |
| 30. #16810369 | C22 | semidirect |
| 31. #16810367 | C22 | semidirect |
| 32. #16810352 | C22 | semidirect |
| 33. #16810352 | C22 | semidirect |
| 34. C53×#500 | C22 | semidirect |
| 36. C53×#492 | C22 | semidirect |
| 37. C53×#486 | C22 | semidirect |
| 38. C82×C53 | C22 | semidirect |
| 126. D424 | D8 | semidirect |
| 189. #1706 | D53 | semidirect |
| 205. #500 | C2×D53 | semidirect |
| 207. #492 | C2×D53 | semidirect |
| 208. #486 | C2×D53 | semidirect |
| 230. C82 | C2×D53 | semidirect |
| 231. C53 | #19884 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20286527 | 2 |
| #20286314 | 2 |
| #20274177 | 2 |
| #20274149 | 2 |
| #20273947 | 2 |
| #20273767 | 2 |
| #20273601 | 2 |
| C8×D424 | 2 |
| C53×#1706 | 2 |
| #19884 | 53 |