Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
740 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 740 conjugacy classes of subgroups — too many to draw. Only its 139 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. #20285060 | C2 | semidirect |
| 3. #20276165 | C2 | semidirect |
| 4. #20276020 | C2 | semidirect |
| 5. #20275888 | C2 | semidirect |
| 6. #20275427 | C2 | semidirect |
| 7. #20275077 | C2 | semidirect |
| 8. #20274677 | C2 | semidirect |
| 9. C53×#1884 | C2 | semidirect |
| 12. #16811180 | C22 | semidirect |
| 21. #16810650 | C22 | semidirect |
| 25. #16810619 | C22 | semidirect |
| 30. C2×#13133128 | C22 | semidirect |
| 31. #16810394 | C22 | semidirect |
| 32. #16810387 | C22 | semidirect |
| 33. #16810379 | C22 | semidirect |
| 34. C53×#568 | C22 | semidirect |
| 37. C53×#410 | C22 | semidirect |
| 38. C53×#339 | C22 | semidirect |
| 228. #1884 | D53 | semidirect |
| 239. #568 | C2×D53 | semidirect |
| 259. #410 | C2×D53 | semidirect |
| 264. #339 | C2×D53 | semidirect |
| 266. C53 | #31280 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285060 | 2 |
| #20284063 | 2 |
| #20276165 | 2 |
| #20276020 | 2 |
| #20275888 | 2 |
| #20275427 | 2 |
| #20275077 | 2 |
| #20274677 | 2 |
| C53×#1884 | 2 |
| #31280 | 53 |