Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
668 conjugacy classes of subgroups; only the 151 normal subgroups are shown.
This group has 668 conjugacy classes of subgroups — too many to draw. Only its 151 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. #20287856 | C2 | semidirect |
| 2. #20286515 | C2 | semidirect |
| 3. #20276965 | C2 | semidirect |
| 4. #20276835 | C2 | semidirect |
| 5. #20276792 | C2 | semidirect |
| 6. #20276674 | C2 | semidirect |
| 7. #20276597 | C2 | semidirect |
| 8. C53×#2170 | C2 | semidirect |
| 9. #16811428 | C22 | semidirect |
| 12. #16811061 | C22 | semidirect |
| 16. C2×D848 | C22 | semidirect |
| 17. C2×D848 | C22 | semidirect |
| 18. #16811000 | C22 | semidirect |
| 20. #16810893 | C22 | semidirect |
| 22. #16810741 | C22 | semidirect |
| 23. #16810453 | C22 | semidirect |
| 24. #16810437 | C22 | semidirect |
| 25. #16810431 | C22 | semidirect |
| 26. C53×#504 | C22 | semidirect |
| 28. C53×#364 | C22 | semidirect |
| 29. C53×#350 | C22 | semidirect |
| 30. C4×C16×C53 | C22 | semidirect |
| 45. Dic424 | D4 | semidirect |
| 47. #13133162 | D4 | semidirect |
| 52. D848 | D4 | semidirect |
| 145. #2170 | D53 | semidirect |
| 160. #504 | C2×D53 | semidirect |
| 168. #364 | C2×D53 | semidirect |
| 171. #350 | C2×D53 | semidirect |
| 172. C4×C16 | C2×D53 | semidirect |
| 173. C53 | #33858 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20287856 | 2 |
| #20286515 | 2 |
| #20276965 | 2 |
| #20276835 | 2 |
| #20276792 | 2 |
| #20276674 | 2 |
| #20276597 | 2 |
| C53×#2170 | 2 |
| #33858 | 53 |