Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
668 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 668 conjugacy classes of subgroups — too many to draw. Only its 135 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. #20287852 | C2 | semidirect |
| 2. #20286514 | C2 | semidirect |
| 3. #20276832 | C2 | semidirect |
| 4. #20276788 | C2 | semidirect |
| 5. #20276671 | C2 | semidirect |
| 6. #20276597 | C2 | semidirect |
| 7. #20276553 | C2 | semidirect |
| 8. C53×#2246 | C2 | semidirect |
| 10. #16811424 | C22 | semidirect |
| 11. #16811059 | C22 | semidirect |
| 16. #16811039 | C22 | semidirect |
| 18. #16810890 | C22 | semidirect |
| 21. #16810741 | C22 | semidirect |
| 22. #16810453 | C22 | semidirect |
| 23. #16810444 | C22 | semidirect |
| 24. #16810436 | C22 | semidirect |
| 25. #16810431 | C22 | semidirect |
| 26. #16810406 | C22 | semidirect |
| 27. C2×D16×C53 | C22 | semidirect |
| 28. C2×D16×C53 | C22 | semidirect |
| 29. C53×#493 | C22 | semidirect |
| 30. C4×C16×C53 | C22 | semidirect |
| 44. Dic424 | D4 | semidirect |
| 45. #13133162 | D4 | semidirect |
| 47. D848 | D4 | semidirect |
| 140. #2246 | D53 | semidirect |
| 158. C2×D16 | C2×D53 | semidirect |
| 159. C2×D16 | C2×D53 | semidirect |
| 161. #493 | 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 |
|---|---|
| #20287852 | 2 |
| #20286514 | 2 |
| #20276832 | 2 |
| #20276788 | 2 |
| #20276671 | 2 |
| #20276597 | 2 |
| #20276553 | 2 |
| C53×#2246 | 2 |
| #33858 | 53 |